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GIS and Archaeological Site
Location Modeling
EDITED BY
Mark W.Mehrer
Konnie L.Wescott
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Dedication
To Jim (glad you’re home safe from Iraq), Jackie, and Allison
–KLW
For Denise, Paige, and Alexander who make it all worthwhile
–MWM

Preface
This volume began as an idea for a conference. The idea was that the goals of
archaeological predictive modeling needed to be reexamined in light of then-current
criticisms, such as: site location cannot be modeled because ancient cultures cannot be
modeled; site location cannot be modeled on the basis of known site locations because
the population of known sites is biased by sampling errors; and, site models based on
environmental factors are environmentally deterministic and therefore fatally flawed.
At the same time, advances in GIS (geographic information systems) software and
personal-computing power had put sophisticated tools in the hands of archaeologists with
an interest in predictive modeling. In other disciplines, GIS was being employed to model
species diversity in forests, predict wetland dynamics, model health-care availability, and
a host of other useful tasks. Surely these other disciplines had provoked profound
criticism of their “fatal flaws.” Yet they persisted and were doing something useful
nevertheless. Perhaps there might be something useful to be done in archaeology by using
GIS in service of predictive modeling if only we could see our way through the criticisms
and neutralize our flaws.
True, it is unlikely that archaeologists will successfully model ancient society because
it is too remote and too many mysteries remain. Also true, we are unlikely to predict the
location of the next important site in the region of our choice because computers cannot
be expected to perform a task that we are unable to formulate with our minds. And yet,
other disciplines were using GIS methods and data to make useful models.
Our conference was inspired by the knowledge that some archaeologists were actually
producing useful models—models that helped land managers and resource planners make
better informed and more reasonable decisions. Other archaeological scholars were
developing new methods and improving old ones. Decision support was a tacit if not
proclaimed goal, the fatal flaws of societal modeling or site prospection notwithstanding.
It seemed like a good time to assemble a broad range of experts to establish a baseline for
site-location models.
And it was a good time, too. The response to our call for papers was gratifying.
Responses came from Australia, Austria, Belgium, France, Greece, The Netherlands,
Slovenia, the United Kingdom, and throughout the U.S. The international enthusiasm was
especially welcome because the Wescott and Brandon (2000) edited volume was due out
and had primarily emphasized the Western Hemisphere.
The conference center at Argonne National Laboratory’s Advanced Photon Source
was an outstanding venue. Its seclusion, security, and excellent facilities no doubt added
to the freedom allowing ideas to readily flow. Our schedule offered plenty of time for
discussion in addition to paper delivery. The discussion time was well used by the
audience, who offered generous responses with lively give and take. After the papers
were delivered, most of the participants were able to stay for an extended discussion
about the immediate future of the modeling endeavor. This, too, was a lively exchange

with an overtone not unlike what you might expect in the first full meeting of a newly
formed organization. Well, we did not actually create a new organization, but I have
noticed that some of the new notions we kicked around are now, 4 years later, mentioned
more often in the literature—notions like “decision-support” and “baseline
establishment.”
Almost all of the presenters followed through by submitting papers for publication.
That is why this is such a hefty volume. Each contribution was well conceived and
professionally written, as I am sure you will agree.
MWM
DeKalb, Illinois

Acknowledgments
We thank all of the contributors to this volume as well as the additional presenters and
participants at the GIS and Archaeological Predictive Modeling Conference (pictured
here). Everyone’s cooperation, support, and persistence are much appreciated. We thank
Northern Illinois University for its financial support and Argonne National Laboratory
for the use of its facility.
Attendees of the GIS and
Archaeological Predictive Modeling
Conference, Argonne National
Laboratory, March 2001. (Courtesy of
Argonne Photo Library)
Mark W.Mehrer
Department of Anthropology
Northern Illinois University
De Kalb, Illinois

Konnie L.Wescott
Argonne National Laboratory
Argonne, Illinois

Editors
Mark W.Mehrer is an archaeologist with research interests in North American
prehistory, settlement studies, household archaeology, remote sensing, and GIS. He
has conducted research in midwestern North America. He is an associate professor in
the Department of Anthropology, Northern Illinois University, where he teaches
archaeology and directs NIU’s Contract Archaeology Program.
Konnie L.Wescott is an archaeologist with Argonne National Laboratory. Her work for
Argonne centers on the environmental assessment process, specifically the evaluation
of potential impacts of proposed federal actions on cultural resources. She is also
involved in activities in support of environmental assessments at various federal
facilities throughout the U.S., such as conducting archaeological surveys, developing
cultural resource management plans, and performing historic-building inventories. Her
research interests include the use of GIS for modeling site locations and performing
impact analyses, as well as Mesoamerican archaeology and museum studies. She is
lead editor of a related book entitled Practical Applications of GIS for Archaeologists,
published by Taylor and Francis in 2000.

Contributors
Matthew Cole Environmental Services, Inc., Raleigh, North Carolina
Christopher D.Dore Cartography and Geospatial Technologies Department, Statistical
Research, Inc., Tucson, Arizona, and Department of Anthropology, University of
Arizona, Tucson, Arizona
Michiel Gazenbeek Centre d’Etudes Préhistoire, Antiquite, Moyen Age, Sophia-
Antipolis (Valbonne), France
Steve Gould GAI Consultants, Inc., Monroeville, Pennsylvania
Trevor Harris West Virginia University, Morgantown, West Virginia
Eugenia G.Hatzinikolaou Department of Geography and Regional Planning, National
Technical University of Athens, Athens, Greece
Carrie Ann Hritz Oriental Institute, University of Chicago, Chicago, Illinois
Hans Kamermans Faculty of Archaeology, Leiden University, Leiden, The Netherlands
Kira E.Kauf mann Department of Anthropology, University of Wisconsin, Milwaukee,
Wisconsin
Frank J.Krist, Jr. USD A Forest Service, Forest Health Technology Enterprise Team
(FHTET), Fort Collins, Colorado
James Kuiper Environmental Assessment Division, Argonne National Laboratory,
Argonne, Illinois
Kenneth L.Kvamme University of Arkansas, Fayetteville, Arkansas
James Levenson Environmental Assessment Division, Argonne National Laboratory,
Argonne, Illinois
Gary Lock Institute of Archaeology, University of Oxford, Oxford, United Kingdom.
Scott Madry Informatics International, Chapel Hill, North Carolina
Christian Mayer Federal Commission on Historical Monuments, Department of
Archäology, Vienna, Austria
Philip B.Mink, II Kentucky Archaeological Survey, Lexington, Kentucky
Jerry Mount Department of Geography, Southern Illinois University, Carbondale,
Illinois
Linda S.Naunapper Archaeological Research Laboratory, University of Wisconsin,
Milwaukee, Wisconsin
David Pollack Kentucky Heritage Council, Kentucky Archaeological Survey, Frankfort,
Kentucky
Ben Resnick GAI Consultants, Inc., Monroeville, Pennsylvania
Malcolm Ridges Department of Environment and Conservation, Armidale, NSW,
Australia
Kevin R.Schwarz Department of Anthropology, Southern Illinois University,
Carbondale, Illinois
Scott Seibel Environmental Services, Inc., Raleigh, North Carolina

Zoran Stančič Institute of Anthropological and Spatial Studies, Scientific Research
Centre of the Slovenian Academy of Sciences and Arts, Ljubljana, Slovenia
B.Jo Stokes Westchester Community College, State University of New York, Valhalla,
New York
Tatjana Veljanovski Institute of Anthropological and Spatial Studies, Scientific
Research Centre of the Slovenian Academy of Sciences and Arts, Ljubljana, Slovenia
Bruce Verhaaren Environmental Assessment Division, Argonne National Laboratory,
Argonne, Illinois
Philip Verhagen RAAP Archeologisch Adviesbureau BV, Amsterdam, The Netherlands
Frank Vermeulen Department of Archaeology and Ancient History of Europe, Ghent
University, Belgium
LuAnn Wandsnider Department of Anthropology and Geography, University of
Nebraska, Lincoln, Nebraska and Statistical Research, Inc., Tucson, Arizona
Konnie L.Wescott Argonne National Laboratory, Argonne, Illinois
Thomas G.Whitley Brockington and Associates, Inc., Norcross, Georgia
Matt Wilkerson Office of Human Environment, North Carolina Department of
Transportation, Raleigh, North Carolina

Contents
Section 1: Introduction
1 There and Back Again: Revisiting Archaeological Locational Modeling
Kenneth L.Kvamme
2
Section 2: Theoretical and Methodological Issues
2 Enhancing Predictive Archaeological Modeling: Integrating Location,
Landscape, and Culture
Gary Lock and Trevor Harris
36
3 One Step Beyond: Adaptive Sampling and Analysis Techniques to Increase
the Value of Predictive Models
Konnie L.Wescott
56
Section 3: Issues of Scale
4 Modeling for Management in a Compliance World
Christopher D.Dore and LuAnn Wandsnider
66
5 Problems in Paleolithic Land Evaluation: A Cautionary Tale
Hans Kamermans
89
6 Regional Dynamics of Hunting and Gathering: An Australian Case Study
Using Archaeological Predictive Modeling
Malcolm Ridges
115
Section 4: Quantitative and Methodological Issues
7 Making Use of Distances: Estimating Parameters of Spatial Processes
Christian Mayer
137
8 Integrating Spatial Statistics into Archaeological Data Modeling
Kevin R.Schwarz and Jerry Mount
154
9 Quantifying the Qualified: The Use of Multicriteria Methods and Bayesian
Statistics for the Development of Archaeological Predictive Models
Philip Verhagen
176

Section 5: Large Databases and CRM
10 Points vs. Polygons: A Test Case Using a Statewide Geographic Information
System
Philip B.Mink, II, B.Jo Stokes, and David Pollack
200
11 Relating Cultural Resources to Their Natural Environment Using the
IEDROK GIS: A Cultural Resources Management Tool for the Republic of
Korea
Bruce Verhaaren, James Levenson, and James Kuiper
220
12 Appropriateness and Applicability of GIS and Predictive Models with
Regard to Regulatory and Nonregulatory Archaeology
Kir a E.Kaufmann
243
13 Archaeological GIS in Environmental Impact Assessment and Planning
Linda S.Naunapper
255
Section 6: Modeling Applications in Progress
14 Understanding Lines in the Roman Landscape: A Study of Ancient Roads
and Field Systems Based on GIS Technology
Frank Vermeulen
266
15 A GIS-Based Archaeological Predictive Model and Decision Support System
for the North Carolina Department of Transportation
Scott Madry, Matthew Cole, Steve Gould, Ben Resnick, Scott Seibel, and
Matt Wilkerson
292
16 Multicriteria/Multiobjective Predictive Modeling: A Tool for Simulating
Hunter-Gatherer Decision Making and Behavior
Frank J.Krist, Jr.
310
17 Predictive Modeling in a Homogeneous Environment: An Example from the
Charleston Naval Weapons Station, South Carolina
Thomas G.Whitley
326
18 Predictive Modeling in Archaeological Location Analysis and
Archaeological Resource Management: Principles and Applications
Tatjana Veljanovski and Zoran Stančič
362
19 The Changing Mesopotamian Landscape as Seen from Spot and Corona
Images
Carrie Ann Hritz
380
20 Quantitative Methods in Archaeological Prediction: From Binary to Fuzzy
Logic
Eugenia G.Hatzinikolaou
403

21 The Use of Predictive Modeling for Guiding the Archaeological Survey of
Roman Pottery Kilns in the Argonne Region (Northeastern France)
Philip Verhagen and Michiel Gazenbeek
411
Index 424

1
There and Back Again: Revisiting
Archaeological Locational Modeling
Kenneth L.Kvamme
1.1 Introduction
Predictive modeling—the practice of building models that in some way indicate the
likelihood of archaeological sites, cultural resources, or past landscape use across a
region—has its roots in the 1960s and earlier. Such models were implicit in the earliest
expressions of settlement archaeology (e.g., Willey 1953) and in later work that actually
formulated explicit statements about prehistoric location (e.g., Williams et al. 1973). The
First Age of Modeling, in the early to mid-1980s, saw many stumbling blocks to be
overcome: ways of thinking that concentrated more on difficulties and sources of
variation that seemed to dictate why archaeological models could not be developed, the
“processualist school” that advocated deductive or “lawlike” behavioral statements as a
basis for modeling and decried uses of statistical methodologies based on simple
correlations, and a lack of effective computer technology for the application of models
across regions. Yet, despite these disadvantages, real progress was made, largely in
university research settings made possible by cultural resource management
(CRM)funded projects. Some of these advances included recognition of sampling biases
in archaeological databases, procedures for characterization of background environments,
applications of univariate and multivariate statistical tests and models, the use of
independent test samples for model performance assessments, and the pioneering
applications of geographic information system (GIS) technology in the discipline (see
Judge and Sebastian 1988; for historical overviews see Kvamme 1995; Wheatley and
Gillings 2002:165–181).
The Second Age of Modeling, now ongoing, is very different in form and orientation.
Readily available digital data and ease of GIS software application facilitate the entire
modeling process, and ample funding has created incentive. There is now a multimillion
dollar archaeological modeling industry, but based almost entirely within CRM settings.
One key benefit of this work has been the collation and standardization of archaeological
knowledge within modeling regions into computer databases; another has been the
building of diverse GIS layers for those regions (Mink et al., Chapter 10, this volume).
Both are of great use to the archaeological community. Yet, given the volume of work
and its scope—archaeological models have been developed for entire states and large
segments of Canadian provinces (e.g., Dalla Bona and Larcombe 1996; Hobbs 1996;
Madry et al., Chapter 15, this volume)—shortcomings exist. Funding agencies may be
willing to support development of modeling applications, but not new research into

methods or more-anthropological interests revolving around the interpretation of results
and the incorporation of findings into the knowledge base of archaeology. Moreover,
much of this work does not get published, and there has been a sameness to approaches
that suggests a lack of innovation beyond basic procedures established during the First
Age. In other words, advances in archaeological location modeling have not generally
kept pace with new methodologies developed in such diverse fields as GIS, satellite
remote sensing, economic geography, and wildlife biology. Fortunately, the chapters that
follow in this volume serve to correct many of these deficiencies.
In this chapter I examine some of the key issues in the First Age of Modeling that yet
impact and impinge on the conduct of modeling today. I hope to clear up several sticky
issues. Being somewhat of a fossil from the First Age, I necessarily digress and offer
some historical background from my own experience in the growth of modeling. Beyond
this, I present a theoretical justification for the practice of archaeological location
modeling, review several important new methodologies that have arisen in the past
decade, and discuss how they might be incorporated within our modeling tool kits.
1.2 Not So in Bongo-Bongo: Cultural Variation and Modeling
Most North American archaeologists are trained within departments of anthropology. The
province of that field claims the full range of variability among all peoples, in all places,
in all times (Hoebel 1966). Such tremendous variation in cultures and behaviors is mind-
boggling to contemplate, and I believe it structures how the anthropologically trained
view the world and approach their research. Focus tends to be placed on variation or
differences between cultures, and in archaeology, the unique artifacts, sites, or dates; the
spectacular find; the oldest; the richest, and the extraordinary tend to receive focus.
In stark contrast, scientific practice in most disciplines focuses on regularities or
patterns, on commonalities, on recognizing order in the chaos of the natural world by
formulating generalizations or rules (laws, principles) of increasing specificity. The
anthropological tendency to concentrate on differences and contrasts among phenomena
stifles such progress, resulting in little more than a compendium of variation. In spite of
this, a large anthropological movement did arise in the mid-20th century that examined
systematic cultural patterns, hoping to elucidate regularities underlying human behaviors.
Known as “cross-cultural methodology” and culminating in such endeavors as the Cross-
Cultural Survey and the Human Relations Area Files, countless cultural patterns and
causal and functional relationships were investigated between such phenomena as types
of social organization and warfare, or form of residence, or environmental type, or
religious practices, and other factors (e.g., see Murdock 1949, 1967). As is always the
case with anthropological data, exceptions to general rules were frequent: a culture or
cultures could be found that did not “fit the pattern.” I am reliably informed that when
George Peter Murdock, a central figure in cross-cultural methodology, was confronted
with the unique society once too often, he exclaimed in exasperation “not so in Bongo-
bongo,” a theme relevant here.
About 15 years ago I decided to investigate this penchant for the unique, this focus on
chaos rather than pattern, by having students in my anthropological statistics class at the
University of Arizona (where I was then employed) undertake an experiment with the
There and back again 3

help of the larger student body. Each student interviewed ten individuals—upper class
undergraduates, graduate students, or faculty—who would have well-inculcated modes of
thought according to their fields of study. Each interviewed five from anthropology and
five from physical sciences like physics, engineering, chemistry, or astronomy. The
interviewees were asked to write a descriptive statement about two similar objects, in this
case a common wooden pencil and a Bic pen.1
The results in no way constitute a random
sample, but I think they are enlightening. About two-thirds of the anthropologists asserted
contrasts or differences in their responses, with statements like “one is green, the other
white,” “one has a metal tip, the other a graphite one,” “one cross-section is octagonal,
the other is circular,” and so on. In the more science-based group, nearly the opposite
occurred, with almost three-quarters seeing commonalities like “both are roughly
cylindrical,” “both have about the same mass,” or “both have a conical tip.”
These perspectives on anthropological thinking are relevant to many of the difficulties
that I and others faced in developing approaches to archaeological locational modeling
nearly a quarter-century ago, and they may even apply today. Instead of focusing on
problem-oriented solutions to modeling human locational behavior, much energy gets
diverted to complaining about the many problems, difficulties, and “deficiencies” of the
archaeological record, or to variations in human behavioral practices, or to insufficient
digital representations or algorithms in GIS, or to the inadequacies of contemporary
maps, and on and on. A list of some of the sources of variation that have been used as
arguments against modeling is given in Table 1.1. (Ironically, most of it comes from the
pioneering collection on archaeological predictive modeling edited by Judge and
Sebastian 1988; more on this volume below.) These many difficulties and dimensions of
variation have served to deflect our attentions away from pathways that might lead to
successful models; they also emphasize the many challenges one is faced with in
modeling past human locational behaviors.
To give a sense of balance, I formulated a similar list containing reasons why we can
pursue models of archaeological location, but it came down to only three simple points.
1. Human behavior is patterned with respect to the natural environment and to social
environments created by humanity itself.
2. We know or can learn something about how people interacted with these environments
by observing relationships between human residues (i.e., the archaeological record)
and environmental features.
3. GIS provides a tool for mapping what we know.
TABLE 1.1 A Few Sources of Variation Posing
Difficulties in the Archaeological Modeling Process
Archaeological
• Many archaeological sites are buried, and we cannot model them because we do not and cannot
know about their distributions
• Known site distributions in extant government files and databases are biased because of (a) the
haphazard way in which many were discovered and (b) variations in obtrusiveness, visibility,
and preservation
• Many known sites are inaccurately located on maps and in databases
GIS and archaeological site location modeling 4

• One cannot model archaeological site distributions because “site” is a meaningless concept;
human behavior did not occur in discrete bounded areas but formed a continuum over the
landscape
• Functional, temporal, or cultural site types cannot be readily determined for most sites in an
archaeological database, yet profound locational differences must exist between the types
• We must be able to model and understand the archaeological formation process, both natural and
cultural, before we can model where sites might be found
Environmental
• Past environments were very different from present ones, so we cannot model the past based on
the present
• Models based on landscape variables are meaningless
• We do not know the locations of resources important in past times, such as water sources,
springs, edible-species distributions, lithic raw material sources, and the like
Behavioral
• Human behavior is too idiosyncratic to be modeled; one cannot model the unique
• One must understand and model complete behavioral systems before archaeological models can
be built
• Site location is more a function of unknown (and frequently unknowable) social environments
representing dimensions that we cannot map
• The most interesting sites are the (idiosyncratic) ones that do not fit the pattern
• Environmental variables shown to be important to site locations may only be proxies for
variables that were actually important
Technical
• Blue-line features on topographic maps are frequently arbitrary and unreliable indicators of
water
• Modern soil types are meaningless because they are changed from the past and, in any case, are
frequently irrelevant to past farming practices
• GIS data have insufficient resolution and poorly represent the real world
• GIS data are inaccurate
• Linear distances computable in GIS are meaningless
• Models based on statistics cannot meet random-sampling assumptions because most extant data
were not obtained by random sampling
• Models derived from random cluster sampling are misspecified because they do not adjust for
underestimated variances
• Grouping sites of many types into a single, site-present class creates too much variability to be
modeled
• Models based on site presence-absence criteria are misspecified because one cannot assume site
absence

1.3 The First Age of Modeling: A Personal Narrative
As a master’s candidate in the mid-1970s, I was excited by the possibilities of the New
Archaeology and assumed that knowledge of statistical methods would go a long way
toward solving the problems of archaeology, as were many of my fellow students.
(Fortunately, we were blessed with a rather good agricultural statistics department at
Colorado State University, in which many of us took classes.) I remember working with
discriminant functions on a lithics problem when a fellow student, Jim Chase (now with
the U.S. Bureau of Land Management, Wyoming), asked me if I thought they might be
applied to environmental variables map-measured at known sitepresent and site-absent
samples to develop a model that might ultimately be employed to make predictions about
archaeological locations. I replied that I thought it a splendid idea, and fortunately
remembered it.
A few years later, while working for a small archaeological company, a proposal
request by the U.S. Bureau of Land Management (BLM) called for (1) a large Class 2
survey (a random sample survey) in the central Rocky Mountains and (2) the mapping of
likely locations of archaeological sites for management purposes, based on patterns in the
sample data. At that time, such maps were typically composed of giant polygons
corresponding to broad environmental tracts like valley bottoms, open grasslands, or
juniper forests, and “predictive” guidance was typically given by estimates of site density
per zone based on survey sample data (Figure 1.1 a). Environmental types with high
estimated archaeological densities were deemed “more sensitive” for management and
planning purposes than zones of low densities (e.g., Camilli 1984; Ebert 1978; Plog
1983).
Our successful proposal, for what became known as the Glenwood project, employed
canonical discriminant functions and, without belaboring details, we generated a model
that appeared on the basis of jackknifed validation tests on the sample data, plus a second
independent data set (also a random sample survey), to offer good performance in the
range of 80 to 85% correct (Kvamme 1980). It is emphasized that all this occurred before
GIS or even personal computers (PCs) were available, so mapping results in the form of a
probability surface was not easily undertaken.
Instead, I programmed the discriminant functions into a Texas Instruments TI-59
calculator, an amazing gizmo that read from or wrote to tiny magnetic strips, and this
program was given to the BLM in lieu of predictive maps. To assess a property about the
potential for archaeological resources, the land manager would go to the proper map,
hand-measure the six relevant environmental variables (e.g., slope, elevation, local relief,
height above river), enter them into the calculator by pressing preprogrammed function
keys, and it would spit out a p-value for that locality (i.e., an estimated probability of
archaeological site-presence conditional on the environmental measurements). This
methodology was actually employed by the BLM to

FIGURE 1.1 Early archaeological
“prediction” maps, (a) A map based on
gross environmental zones with
estimates of likely site density (after
Plog 1983). (b) An early, precompiler
age, hand-drafted archaeological
probability surface (after Kvamme
1980). (c) The first archaeological
probability surface derived completely
through computer measurement of map
variables (after Kvamme 1983).
assist in property assessments for a number of years. It was of some significance that this
model could be applied to characteristics associated with a point on a map, because
previously the resolution of most models was at the level of the environmental zone or
community, typically many hectares (or even square kilometers) in area (Figure 1.1a).
The idea of producing a mappable archaeological probability surface was in my mind,
however, and our team was bent on including one in our final report (Kvamme 1980). We
did so by enlarging a single quarter-section (quarter of a square mile; about 800×800 m)
that contained three archaeological sites independently discovered by another project. We
superimposed a 50×50-m grid, producing a 16×16 matrix of 256 cells, and in each we
hand-measured the six predictor variables of the model, for 1536 measurements. Lacking

a PC, and with the nearest mainframe computer more than 150 km away, we elected to
spend an afternoon with our TI-59 and entered the six measurements for each cell by
hand to generate the 256 p-values. Finally, we hand-drafted a probability surface that,
pleasingly, corresponded well with our notions about the most likely places where
archaeological sites would be found (based on years of experience in the area), and with
the known site locations (Figure 1.1b).
This exercise convinced me that (1) our archaeological modeling methodology was far
superior to any other approach then available; (2) the model itself, the statistical analyses
leading up to it, and its mapping offered great potential for understanding human-
environmental interactions; and (3) an automated mechanism was absolutely necessary to
map the model functions over broad regions. In 1980 I returned to graduate school for a
doctorate at the University of California at Santa Barbara to study with Michael Jochim,
whose then-recent book Hunter-Gatherer Subsistence and Settlement: A Predictive
Model (1976) was of prime relevance (this work offers a rare example of an
archaeological model derived through mathematical deduction); with Albert Spaulding,
the founder of statistical reasoning in archaeology; and to study in the university’s
Department of Geography, then leading the country in quantitative geography and
computerized map handling, later to grow into GIS.
Without GIS software in 1980–1983, we employed a computer system for handling
satellite data known as VICAR (video imaging communication and retrieval) that was
connected with something called IBIS (image-based information system), which allowed
special-purpose FORTRAN subroutines to be linked through horrendous IBM JCL (job
control language), all on punch cards. I became a programmer. Without scanning
technology and no readymade digital maps, I first learned to communicate with digitizers
so that digital representations of elevation contour lines could be produced, and
ultimately a DEM (digital elevation model) after interpolation. FORTRAN routines were
written for computing slope, aspect, local relief, ridge and drainage lines, terrain
variance; generating distance surfaces from stream vectors; and other operations. While
working on this embryonic GIS, I was able to computer-generate my first archaeological
probability surface, presented at the annual meeting of the Society for American
Archaeology (SAA) in 1981, with improvements in subsequent meetings (published in
Kvamme 1983; Figure 1.1c).
At those SAA meetings, I made two important contacts. One was Sandra Scholtz (now
Parker) of the Arkansas Archeological Survey, who had been independently developing a
nearly identical modeling methodology in their Sparta Mine project, in Arkansas. Their
big stumbling block was also the lack of an automated means to measure map variables,
but with a circumscribed area, they were able to hand-measure a suite of relevant
environmental variables within grid cells 200 m in size (to reduce the number of
measurements), from which they generated prehistoric- and historic-site probability
surfaces using SAS statistical software (Scholtz 1981; Parker 1985). They were using a
relatively new and more robust classification algorithm known as logistic regression
(based on the recommendation of James Dunn, Department of Mathematics, University
of Arkansas), which proved fortuitous, because Alan Strahler, who pioneered
applications of logistic regression in remote sensing (Maynard and Strahler 1981), held a
visiting professorship at UC-Santa Barbara the following year. My second important
contact was Bob Hasenstab, then a student at the University of Massachusetts (now at the

University of Illinois-Chicago), who had also programmed a GIS from scratch, in
FORTRAN, to enable cultural resource modeling studies of high resolution in the Passaic
River area of New Jersey (Hasenstab 1983). These and other associations led to the first
GIS and archaeology symposium, held at the 1985 SAA meeting and quaintly titled:
“Computer-Based Geographic Information Systems and Archaeology: A Tool of the
Future for Solving Problems of the Past.”
Post-doctorate employment took me to the University of Denver, where I became
involved in the volume Quantifying the Present and Predicting the Past: Theory, Method,
and Application of Archaeological Predictive Modeling (edited by Judge and Sebastian
and completed by 1985, but not published until 1988). Government-sponsored project
authors (often part of consulting firms) had to be part of successful proposals in a
national competition, a fact that was certainly one ingredient that contributed to ensuing
problems, because individuals who should have been part of it either did not bid (they did
not know about it) or did not submit competitive proposals. Ironically, many that
ultimately joined the project had little or no previous experience in archaeological
location modeling. The result was considerable chaos, leading to its many-year delay to
publication and to issues still influencing contemporary work that warranted closer
scrutiny.
Several editors and authors of Quantifying the Present and Predicting the Past were
ardent followers of the processualist school of archaeology (devoted to understanding
elements of culture process or change), who informed us that only models generated
through deductive reasoning were “good” and potentially “explanatory,” while models
utilizing statistical methods were not only “inductive” (a bad word at the time), but
“merely correlative” and incapable of explanatory insight. Furthermore, it was asserted
that “models must span the entire explanatory framework rather than simply
concentrating on those things we want to predict…. It is human organizational systems
that must be modeled, as well as all those complicating factors between the highest level
of human behavior and the archaeological record” (Ebert and Kohler 1988:105). This
seemed a tall (and naïve) order to fill that, if followed, left archaeological modeling dead
in the water before it could even leave port. I was stunned because not only had I and
others already developed “successful” models by 1984 (e.g., Kvamme 1980, 1983; Parker
1985; Scholtz 1981) (Figure 1.1b and Figure 1.1c), but I believed (and still do) that (1)
the type of lawlike or rule-based statements that were advanced as “deductive” models
are practical for understanding only relatively trivial cultural processes, (2) such simple
models are unsuitable for applications owing to their comparatively low power (and in
any case none existed that could be applied), and (3) that there was a complete
misunderstanding of the role of statistical methods in applied research settings, points
that I tried to convey in my principal chapter (Kvamme 1988a). Since its publication,
along with several papers a few years later (Kvamme 1990a, 1990b, 1992), my interests
in modeling have only recently been rekindled by an unlikely source: working with
students of biology, I have become aware of a tremendous renaissance in modeling
approaches made possible by the GIS revolution, as the following sections will
demonstrate.

1.4 Perspectives on “Correlative” and “Deductive” Models
Critics of archaeological models derived through statistical methods such as discriminant
functions or regression are wrong in assuming they are based solely on “mere
correlations.” This can rarely be the case because even the simple act of selecting
variables for analysis demands an a priori theoretical perspective that comes from
previous work, training, and exposure to the theoretical currents of a discipline. Statistical
models should most properly be viewed as a means of estimating appropriate weights for
theoretically derived variables. Without such a mechanism it is unlikely that robust
weights can be derived, resulting in models of lower power. A deductive model based on
anthropological theory, previous findings, or ethnographic analogs might define variables
relevant to past location behaviors. But without recourse to statistical calibration based on
sample data, how those variables might be combined, weighted, or thresholded to achieve
a GIS mapping becomes something of an art. A simple Boolean combination, for
example, means that each variable receives an equal and arbitrary weight of unity;
altering those weights in a more complex model implies a level of theoretical knowledge
not generally possible. Moreover, such models must perform suboptimally compared
with those with weights derived from statistical theory and suitably constructed random
samples. Making claims about the superiority of the former is therefore ironic. Dalla
Bona and Larcombe (1996) deduced an excellent suite of variables through ethnohistoric
and contemporary native informant accounts concerning prehistoric settlement in
northwestern Ontario, for example, but their GIS mapping was only possible after close
calibration of model weights against empirical archaeological distributions.
Wildlife biologists utilize GIS to map models of species distributions and habitat
(analogous to archaeological sites) with the advantage of a more mature view of the
modeling process (being firmly wedded to empirical data and possessing a statistical
tradition that goes back to the 19th century). Most biological models begin with theory,
usually meaning a list of variables relevant to the locations or habitat of the species of
interest derived from prior knowledge and work. Based on species locations observed in
field data, the resultant models, including discriminant and logistic regression functions,
give insights into interactions between variables, identify significant relationships,
confirm or refute hypothetical associations, and expose relative strengths of relationships.
Additionally, GIS mappings in the form of species probability or abundance surfaces
prove insightful because relationships between species and environment become
graphically clear, revealing the relative clumping, dispersion, or patchiness of the result
(e.g., see Bian and West 1997; Clark et al. 1993; various papers in Scott et al. 2002).
Khaemba and Stein (2000:836), for example, state outright that their models are
deductively derived because they begin with the prior knowledge that “elephants
generally prefer tall grassland and shrubby vegetation.”
How is the foregoing different from deducing that settlements of a farming culture
should be situated in well-watered valley bottomlands, near level fields with good soils?
Wheatley and Gillings (2000:166) observe that
A distinction between data and theory [driven models] is not universally
recognized, and most archaeologists accept that the two are not
independent—data is collected within a theoretical context, and so may be

regarded as theory-laden, while theories are generally based to some
extent on empirical observations…. It is impossible in any practical sense
to implement a predictive modeling method that is based entirely on either
of these tactics.
The archaeological dichotomy that has arisen claiming distinct correlative and deductive
approaches to modeling is an unfortunate historical accident; they need not be different
but can and should be one and the same.
1.5 Theoretical Justification of Archaeological Location Modeling
1.5.1 Background Concepts
In developing models, we need to be clear whether we are trying to model the systemic
context or the archaeological context, as originally codified by Schiffer (1972). The
former refers to the living, behavioral state of a human group or society. The latter refers
to the static, nonbehavioral state of archaeological materials, the physical record that
archaeologists study. Even a perusal of the literature on modeling suggests that it is
frequently unclear which context is being modeled, despite critical differences in
assumptions, approaches, likely difficulties, and possible outcomes. Explanatory or
deductive models appear to be generally concerned with the systemic context, but from a
cultural resource management standpoint the goal clearly seems to be the modeling of the
archaeological context.
In approaching the latter, we must first recognize that if a goal of modeling is the
mapping of locations where archaeological resources are likely to occur, then logically
the equivalent is the mapping of locations where such resources are unlikely to exist. The
elimination of portions of a region that are unlikely to contain archaeological resources
becomes a useful way of approaching the modeling problem.
The definition of the niche of a species, as defined in quantitative ecology, provides a
second vital perspective. The niche can be defined as the total range of conditions in the
environment under which a population lives and replaces itself (Pianka 1974:186). In a
landmark paper, Hutchinson (1957) emphasized that the niche can be determined
empirically by measuring the location of individuals of the population along multiple
dimensions of environment, with the range defining a niche space in a “hypervolume” of
measurements. That space can be visualized as a variable probability density function
(PDF), with certain locations within it more ideal for the species than others. In fact, the
“ideal habitat” of a species can be represented by the mean vector of measurements on
each variable, as indicated by the locations of the species itself. Less desirable habitat is
then inferred as any deviation from the mean vector. (This perspective forms the basis of
an important modeling approach discussed in Section 1.7.3.) The obvious application of
this perspective to ideas of human niche spaces and settlement distributions was first
extended to the field of geography by Hudson (1969). Of more importance are the
implications it offers as a logical basis for archaeological modeling (see Kvamme, 1985
for an early attempt).

1.5.2 A Deductive Model
Let us begin with three observations:
Observation 1: The human organism lives within the natural environment.
Observation 2: The environmental variation within any circumscribed
region is large.
Observation 3: The niche of the human organism is that portion of the
environment that it utilizes or to which it has access.
The human niche, N, may correspond with the entire environmental range, E, of a region,
where the niche space equals the environmental space, N= E. The niche space, however,
may typically include only a subset of the total environmental space, N<E, because areas
of steep slopes, cliff faces, water bodies, lava fields, glaciers, wetlands, high altitudes,
dense vegetation, and other contexts may be inaccessible or unutilized (Figure 1.2). The
level of niche space accessibility may also be partially dependent on technological level,
other cultural circumstances, and resource distributions. For example, cliff faces might
harbor an important food resource (bird eggs) that become accessible only with
appropriate technology (sturdy ropes).
Corollary 1. If N<E, then locational modeling must be productive if N can
be defined.
The analysis of empirical archaeological distributions through a host of statistical or other
means (e.g., Kellogg 1987; Kvamme 1990c) can potentially indicate favorable and
unfavorable localities. Favorable places generally correspond with specific classes of
activity, fitting well with the idea that the PDF is multimodal.
Observation 5: If we do not include simple travel between locations, then
activities are tied to places. Various types of human activity are frequently
associated with particular environmental circumstances.
Fishing occurs in or adjacent to streams or lakes and nut gathering where nuts grow, for
example.
Corollary 3. The association between particular activity classes with
specific environmental contexts dictates that modeling specific sitetype
distributions must be productive. These activity-specific “niches“comprise
small subsets, Ai, within the human niche space, N (Figure 1.2). Each are
determined by relatively few environmental dimensions according to
specific activity needs.

FIGURE 1.2 The human niche,
activity, and habitation spaces can be
viewed as subsets of increasing
specificity within the total
environmental range of a region.
The creation of distinct models for individual types of archaeological sites (functional,
temporal, or other) is something rarely undertaken in the literature of modeling, yet it
forms an area of certain improvement.
Corollary 4. The sum or union of all places where people concentrate
activity forms an activity space, A=ΣAi, that is smaller than the human
niche space (i.e., A<N) if simple travel between places is disallowed
(Figure 1.2). This forms the logical basis of Corollary 2.
Observation 6: Places of human habitation or settlement, with long-
term needs and variable activities represented, must be sited according to
many dimensions of environment dictated by the many needs of
community.

A long-term settlement might be located according to its needs for defensibility and
proximity to water and quality of agricultural soils and level slope and fuel resources,
etc.
Corollary 5. Habitation activities with many location requirements may
be more predictable than sites of specialized activities with relatively few,
defining a comparatively small “niche.” Owing to this fundamental
difference, a habitation space, H, is defined, where H<A (Figure 1.2).
If a simple activity, Ai, requires only environmental condition e1 to occur, but H requires
e1∩e2∩e3∩e4, then generally H<Ai.
Observation 7: People also construct a social environment that influences
locational behavior. If the natural environment defines a possible range of
conditions for the placement of activities, then the social environment
imposes further restrictions and order. Road networks and the necessity of
intersettlement spacing, for example, further alter the PDF within the
human niche space.
Corollary 6. Consideration of variables of the social environment must
be productive because the range of variation within suitable areas or
favorable spaces in the natural environment becomes further reduced.
1.5.3 Summary
The foregoing suggests that if we can view human uses of space in terms of subsets of
environmental variation, and identify those subsets as a basis for modeling, then
archaeologically useful results must be possible if we consider “useful” to mean the
elimination of regions unlikely to contain archaeological resources. Consideration of
individual site types and variables of the social environment will allow models to focus
on narrower ranges of variation, improving performance, and long-term habitations or
settlements should be highly predictable owing to their more restrictive environmental
requirements. To achieve the full potential of this perspective, a number of continuing
issues and methodological improvements must first be addressed.
1.6 The Second Age of Modeling: Continuing Issues
With nearly a quarter-century of serious work in archaeological location modeling, it is
clear that several issues, some of which may be insurmountable, remain at the forefront
of difficulties. They include the problems of modeling multiple site types,
paleoenvironmental reconstructions, and sampling issues. Lack of resolution in these
areas continues to affect the power and specificity of models and, indeed, what we are
able to model.

1.6.1 Archaeological Site Types
A handful of lithics, a couple of sherds, or a few tools gained through a limited surface
reconnaissance does not usually allow reliable reconstruction of the kinds of activities
that occurred at an archaeological site, identification of the culture(s) that used or
produced the artifacts, or accurate estimates of the amount of activity that occurred,
length of occupation, or dates of use. This dilemma, typical of the vast majority of sites in
any region, has forced modelers to throw them into one large “pot” that can only be
labeled “human activity present,” or to ignore them, relying solely on well-dated and
understood sites. The latter tactic is undesirable because the sample size of known
archaeological locations becomes so reduced that meaningful statistical analyses become
untenable. The former is the principal reason why most models remain dichotomous (i.e.,
site-present versus site-absent).
Ethnography and common sense indicate that sites associated with various functions
are located differently: a fishing spot, a plant-gathering location, a hunter’s kill and
butchering site, and a long-term settlement will generally be located in unlike places.
Moreover, different cultural groups may have unique responses to the same environment,
with large variations in locational behavior. Finally, temporal differences between sites
may correlate with vastly changed environmental circumstances. It seems obvious that
when placing all sites in a single group for modeling, the enormous variation associated
with all human activity yields models of lower power and specificity What we end up
modeling is the sum total of the human “activity space” of Figure 1.2. In defense, it must
be noted that models of surprising power have nevertheless been created following this
simple site-presence–absence approach. Brandt et al. (1992), for example, lumped sites of
all types and periods in the Netherlands into a single class (representing a remarkable
breadth of functions, cultures, and chronology) and achieved models that performed
surprisingly well (suggesting some sort of commonality to locational behaviors or
perhaps site visibility).
Defining meaningful site types and modeling each as a separate class is probably the
greatest potential improvement to the quality of archaeological models (see Stančič and
Veljanovski 2000 for an excellent example). Aside from better recording, more field
time, increased funding, retrieval of larger samples of artifacts, better analysis methods,
and improved theory that might point to site function, there appears to be few ways out of
this quandary. Larger, more permanent settlements are sometimes more visible, enabling
models of settlement location (i.e., the “habitation space” of Figure 1.2) as opposed to all
site locations (the “activity space”), a useful undertaking.
One certain area of improvement lies in removing rock shelters or cave sites from
consideration in the modeling equation. These kinds of sites were invariably utilized for a
range of activities, yet unlike all other archaeological sites, their placement in the
landscape is not dictated by human choice. Rather, the loci of rock shelters and caves are
determined by a peculiar and idiosyncratic set of geological variables, including rock
type, exposure, hydrology, terrain shape, and other factors. We can model human choices
that placed other kinds of sites in the landscape, but to model the use of rock shelters and
caves, complex geological models and variables must be pursued that undoubtedly open
up other problems. These sites should therefore not be considered with other site types in
combined modeling operations because the larger range of locational variance introduced

will upset model performance. The best approach for handling them may simply lie in
improved mapping that locates caves and rock shelters.
1.6.2 The Paleoenvironment
Research has demonstrated significant empirical and theoretical relationships between
environment and archaeological distributions. Yet, in nearly all cases, it has been modern
environmental conditions instead of past circumstances that have been investigated. In
most regions, contemporary conditions are very different from those of the past,
especially the distant past, raising the question of just how well models based on the
present situation can predict the past. After all, it was then-contemporaneous conditions
that were relevant to locational decisions and choices made by past peoples. While it can
be argued that terrain form (and its many derivative measures) is relatively stable through
time, it is well-known that plant communities migrate up and down altitudinal clines with
climatic change and that rivers and streams wildly meander within valleys over relatively
short periods, for example.
It would seem that reconstruction of paleoenvironments is a necessary first step in the
archaeological modeling enterprise (see Kamermans, Chapter 5, this volume).
Paleoclimatic data from tree rings and other sources might be employed to model life-
zone altitudinal changes, pollen data could point to former environmental compositions,
and erosion and hydrological models could be used to reconstruct past landforms and
stream channels, for example.
When one considers that paleoenvironmental reconstructions are potentially necessary
for each time period relevant to the archaeological sites in a region, however, such a task
becomes daunting and has rarely been undertaken (for exceptions, see Boaz and Uleberg
2000; Gillings 1995; van Leusen 1993; Nunez et al. 1995). Moreover,
paleoenvironmental and paleoclimatic reconstructions are difficult and capable of only
very broad generalizations, with little specificity in terms of the point-by-point
requirements of GISbased models. (We ideally want representations of the
paleoenvironment on a pixel-by-pixel basis.) Also raised is the question of error budgets
in GIS models based on such data. Recent work has shown significant levels of error,
even in present-day maps (see Goodchild and Gopal 1989). Past reconstructions of an
environment will likely contain huge errors owing to their imprecision. Because error is
cumulative in a multidimensional model, it is quite likely that results could be unusable.
For example, even assuming an unrealistic 90% level of accuracy (however accuracy
might be defined), with only five reconstructed environmental layers, the overall
accuracy becomes .95
=.59, dismal indeed. Unless reliable paleoenvironmental
reconstructions can be generated, it is clear that we must proceed with caution. At the
same time, it might also be argued that any paleoenvironmental reconstruction, however
poor it might be, must be better than using present-day data.
Most practitioners will continue to employ present-day maps and digital data sets as a
basis for modeling, if only because of ready availability. One benefit is that map error is
at least known and quantifiable. Focus should be given to variables less sensitive to
change, such as landform characteristics. Other tactics might also be employed to
mitigate the effects of change. For example, instead of using distance measures to current

rivers or streams (assuming proximity to water is a meaningful criterion), distance to the
edge of the floodplain might instead be considered to eliminate the effects of meandering.
1.6.3 Sampling
Most regional models necessarily employ extant records of archaeological sites from the
region of interest. Sampling biases that exist in these data sets are well-known and arise
from such circumstances as (1) the tendency of archaeologists to discover sites where
they believe they should be or in places with easier access (near roads, towns), (2) the
arbitrary but nonrandom locations of development projects that have required cultural
resource surveys, or (3) the greater obtrusiveness of larger sites and settlements (e.g.,
sites with mounds or earthworks). Models based on these kinds of databases are biased,
and entire archaeological contexts may not be well represented (see Kvamme 1988b for
ways to reduce or mitigate such biases; Wescott, Chapter 3, this volume, discusses
sampling issues).
Some archaeological projects have had the luxury and budgets to employ random
sampling designs and pedestrian surveys to procure unbiased samples for model
development (e.g., Thomas 1975; Warren and Asch 2000). Most have employed some
form of cluster sampling, conducting surveys within randomly selected blocks of large
size (e.g., 500-m squares, quartersections). One reason is convenience: it is easy to locate
a relatively small number of large quadrats on a map and on the ground. Yet, sampling
elements like archaeological sites within clusters creates negative consequences, such as
(1) reduced estimates of variability (because places sampled occur in a relatively small
number of clusters), and (2) a lack of independence between data elements owing to their
spatial proximity or the autocorrelation effect (Kvamme 1988a).
In the past decade we have moved into a very different world where we can now
accurately locate ourselves through GPS (global positioning system) technology. Let us
throw out large cluster blocks and utilize small (subhectare) parcels (or even points) for
survey and random-element sampling designs (Scheaffer et al. 1979). With preselected
coordinates, it is simply a matter of pressing “go to” on the GPS to reach a new locality,
and a survey of nearby randomly selected places can be preplanned to minimize travel
requirements. In so doing, we can attempt to attain “ideal” sampling designs that allow
meeting of statistical assumptions, permit more-representative sampling of environmental
and archaeological variability, and increase the likelihood of independence between
observations.
1.7 The Second Age of Modeling: Possible Improvements
Although much contemporary modeling work is of high quality and innovation is
apparent, other refinements seem possible in such areas as developing new variables
through GIS, utilizing new modeling approaches and algorithms, and in methods for
evaluating model performance. The following subsections offer a number of ideas,
suggestions, and new methods that might be utilized in archaeological locational
modeling.

1.7.1 Independent Variables
Acquiring better data and variables that might bear on archaeological locations is one
domain that can improve our ability to model. As technology improves, our potential in
this area is increased. High spatial resolutions for digital elevation and satellite data mean
that we can capture more detail of the landscape that could be relevant to certain classes
of past activities, for example. Moreover, a lack of consideration of the social
environment has been justly criticized by European scholars (Gaffney and van Leusen
1995), pointing to other dimensions for improvement.
1.7.1.1 The Natural Environment
Variables that quantify aspects of the natural environment will generally remain most
important in archaeological location modeling owing to their ready availability in digital
or map form and their importance to human locational behavior. In general, we need to
move beyond simple terrain variables like slope and aspect, or linear distances to blue-
line water features on maps. We now have access to powerful GIS tools that offer
potentially more. We should pursue quantification of subtle variations in terrain shape
and complexity, identify local high points and saddles (Duncan and Beckman 2000),
quantify solar insolation, terrain texture, and local relief changes above and below
locations for possible relationships with past activities, particularly in hunter-gatherer
contexts. Llobera (2000) and Bell and Lock (2000) reveal great improvements in
modeling movement over the landscape; perhaps it is now time to move beyond simple
linear proximity measures.
One particular area of promise lies in drainage runoff algorithms that objectively
define flow based on landform shape in DEM (Burrough and McDonnell 1998:193–198),
allowing movement away from the frequently subjective and arbitrary blue-line features
on topographic maps. They allow quantification of accumulated flow to any pixel in a
region; simple reclassification methods can then define drainage networks of any rank or
complexity for proximity-based analyses. The continuous scale of accumulated flow
itself might also be of interest.
Vegetation and biomass-biocomplexity diversity indices derived from satellite
imagery are yielding much insight into patterns of regional plant productivity and health
(Sabins 1997:404). They have been largely ignored in archaeological modeling (see
Gisiger 1996, however), despite their apparent potential, particularly in the large tracts of
land in the Americas and elsewhere little changed from recent prehistory.
1.7.1.2 The Social Environment
Social variables typically refer to characteristics of the human-created environment. In
complex societies it is markets, central places, intervillage spacing, road networks,
political boundaries, and the like that drive uses of space. The relative importance of the
natural versus social environments to locational behavior strikes some sort of balance,
with one or the other more important, depending on needs and the nature of activity
requirements. In general, we might imagine a continuum where the relative influence of
these domains is a function of cultural-technological complexity (Figure 1.3, while
realizing that such a generalization may not apply to Bongo-bongo). While both are

important to any society, in hunter-gatherer contexts the social environment probably is
less so, if only because there frequently are no
FIGURE 1.3 The relative importance
of natural versus social environments
to locational behavior is related to
cultural complexity.
markets, central places, road networks, and related phenomena that characterize settings
of greater cultural complexity.
Social variables have rarely been employed in archaeological location modeling
(Gaffney and van Leusen 1995). One reason lies in data availability. Maps of the natural
environment (albeit the present environment) are easy to obtain, and frequently can be
instantly downloaded through the Internet. This is not true of social variables, where the
loci of contemporary villages, markets, religious centers, or roads are frequently difficult
to obtain for past times. In general, it is only in well-studied archaeological regions
where, after decades of work, a reasonable semblance of past social landscapes can be
reconstructed. Yet, even in these ideal contexts, such reconstructions are likely only
partial: missing villages, road segments, or unknown political boundaries are likely (see
Vermeulen, Chapter 14, this volume).
A somewhat more subtle issue lies in the need to establish contemporaneity between
features in the social landscape. Measuring proximity to a road or political center is only
relevant if those features are coeval with the social milieu being modeled. This
requirement further restricts consideration of many social variables to well-studied
archaeological regions with good chronological control. Madry and Rakos (1996) were
able to model prehistoric travel routes based on the arrangement and viewsheds of a

series of contemporaneous Celtic hill forts in France. Chadwick (1978, 1979) was even
more restrictive by modeling Late Helladic settlement distributions based on the
distribution of settlements in preceding periods in Mycenae.
Obviously, archaeological location models that fail to address the social dimension
owing to a lack of data or effort only get at a portion of the variability in past site-
selection behaviors (Corollary 6, above): that portion related solely to the natural
environment, which can be small (Figure 1.3). Recent debate and applications in this
area, particularly by Europeans (with generally better knowledge of archaeological
regions), are therefore encouraging (Gaffney and van Leusen 1995; Gaffney et al. 1995;
Stančič and Kvamme 1999; Wheatley 1996).
1.7.2 Other Modeling Algorithms
With the growth of GIS technology and its ready acceptance by government, industry,
and academia, together with intense focus on regional modeling in other disciplines like
biology, medical science, and economics, there has been a remarkable explosion in
modeling methods and algorithms in the past decade. Approaches in this literature range
from simple Boolean intersections, to additive binary layers, weighted additive layers,
fuzzy versions of the foregoing, Dempster-Shafer models, log-linear and logit models,
dominant-category clustering models, neural-network algorithms, Mahalanobis D2
statistics, suites of classifiers from image-classification methodologies like maximum
likelihood, and the ever-popular discriminant functions, including logistic regression, to
name a few (e.g., Bian and West 1997; Clark et al. 1993; Eastman et al. 1995; Gabler et
al. 2000; van Manen et al. 2002; Vila et al. 1999; Wang 1990).
Despite this great variety of available approaches for modeling many types of spatially
distributed phenomena, there has been relatively little variation in the archaeological
literature in the methods that have been employed. Logistic regression, a robust
nonparametric classifier, has been particularly popular in archaeological model
development, as has discriminant-function analysis, the parametric alternative (Parker
1985; Scholtz 1981; Kvamme 1983, 1988a; Warren and Asch 2000; Wheatley and
Gillings 2002:172). Both are examples of linear statistical models, and even here, recent
improvements exist. Generalized additive models (GAM) appear to offer a significant
advance over the generalized linear model, for example, because they replace the linear
component of the model with an additive one that identifies and describes nonlinear
trends and threshold effects, which are far more common in nature than linear ones
(Hastie and Tibshirani 1990).
1.7.3 Forget Those Nonsites: Single-Class Approaches
As a means of modeling the archaeological context, the two-class approach can be
justified because there are places that contain material evidence of past activities
(archaeological sites) and others that do not (nonsites). Yet, even if thorough field
investigation fails to encounter archaeological evidence at some locus, there is a nonzero
probability that archaeological remains may actually be present; for example, they might
be buried, be lying under vegetation, or simply have been overlooked.

A similar perspective arises in the modeling of biological species occurrence. Much
like the archaeological site present-absent dichotomy, such studies employ sightings or
radiotelemetry on tagged animals to compare their presence-absence against mappable
habitat variables in GIS settings. Logistic regression-based and other probability surfaces
are then developed for species presence (Bian and West 1997; Dettmers et al. 2002).
Argument has recently been vigorous against use of a species-absent class for model
calibration, however, because the lack of a den or nest at the time of a field investigation
does not imply its absence in times past or future (Clark et al. 1993; Dettmers and Bart
1999).2
This quandary has led to alternative modeling approaches of great power that fit
well within long-held theoretical perspectives stemming from perspectives on niche (as in
Figure 1.2).
These approaches focus on a single species-present class (analogous to an
archaeology-present class). Calibrating to a species-present sample, the mean on any one
environmental variable represents an estimate of “ideal habitat” for that species on that
variable; in a multivariate context, it is the mean vector µ that represents ideal habitat
across a series of variables. Less desirable habitat is inferred by any deviation from µ,
agreeing well with the classic species niche model developed by Hutchinson (1957) that
emphasizes an ideal “niche-space” within an n-dimensional hypervolume of relevant
envi-ronmental parameters. The most common metric for evaluating locations in this
perspective is the Mahalanobis distance statistic (in matrix notation)
D2
=(x−µ)′Σ−1(x−µ)
which is interpreted as a squared normalized distance between a location’s measurements
(x) and µ (Σ is the variance-covariance matrix). While D2
is a valid metric on its own, it
tends to be highly skewed, and a χ2
transformation allows a 0-to-1 rescaling that, if
multivariate normality is assumed, can be interpreted as a p-value analogous to a
posterior probability obtained with more-conventional discriminant or logistic regression
functions. These D2
or p-values are then mapped by GIS on a pixel-by-pixel basis,
yielding a “deviation from ideal habitat” or a species-probability surface, respectively
(e.g., Clark et al. 1993; van Manen et al. 2002).
While offering an alternative to more-conventional and -accepted methodologies, this
approach presents its own series of problems. One cannot undertake a stepwise F-to-enter
solution, for example. One has to know which variables are relevant and go with them,
but this does not appear to be a problem in the biological sciences. As alluded to earlier,
variables selected are typically derived from a priori theoretical ideas.
1.7.4 Models of Greater Specificity
Environmental variation in large project areas can be enormous, and past human
adaptations and uses were undoubtedly numerous. Given the size of some projects (e.g.,
whole states and significant proportions of Canadian provinces), gradients or differences
in cultural practices, or even cultural types, might occur, and variables relevant in one
subarea might not even apply to another. A model fine-tuned to the more limited
variation of a small region should theoretically better “fit” that region’s cultural and
environmental variability compared with a global model that can only “average”
relationships over huge areas. To illustrate, I built one logistic regression model using all

data from a 600-km2
region, and then a second model using data only from an 8.5×5.5-
km subarea. The model for the latter, because it dealt only with the archaeological and
environmental variation in the subarea, offered a much better fit with the data, and all
performance indicators were markedly higher (Figure 1.4; Kvamme 1988a).
One might therefore consider partitioning a large project area into a series of small
blocks and building a fine-tuned model for each. Such distinct and independent models
would undoubtedly perform better, but arbitrary “seams” or discontinuities in model
results would likely occur at borders between the individual blocks. Such effects arise
from environmental and archaeological differences between the blocks, resulting in
reduced interpretability and quality of presentation. (Defects like massive jumps in
estimated archaeological probabilities can only be explained by the arbitrary locations
FIGURE 1.4 Archaeological
probability surfaces obtained through
logistic regression analyses of open-air
lithic scatters in an 8.5×5.5-km (46.75
km2
) study block in southeastern
Colorado (after Kvamme 1988a). (a)
Model derived from all open-air lithic
scatters (n=269) and environmental
variation in a larger 600-km2
project
area, (b) Model derived only from data
occurring within the smaller study
block (n=95). (c) Distribution of

known open-air lithic scatters in study
block. Black signifies high
archaeological probabilities.
of boundaries between the study blocks.) With the significant computing power at hand
today, an alternative approach may be workable. A moving window, kilometers in
diameter, could potentially be employed to build a model utilizing data that only occur
within it. The window would then be centered location-by-location throughout the project
area, causing model results at each locus to be based on environmental and
archaeological characteristics that are the most relevant, resulting in models of greater
specificity. Other benefits could potentially accrue from such an approach. Mean vectors,
confidence coefficients, and model parameter estimates within each window could be
mapped and examined over space. Variations in the relative sizes and signs of regression
coefficients, for example, could point to the relative importance of particular variables as
environmental and archaeological circumstances change across a region.
1.7.5 Measures of Model Performance
It is uniformly agreed that a model must be tested before one can place reliance in it, and
this stricture should apply to any model regardless of its means of derivation. Various
methods of resampling (e.g., cross-validation, jackknifing, bootstrapping) have been
developed that can provide robust estimates of performance (Verbyla and Litvaitis 1989).
The ultimate test, however, is against samples independent of those used to develop a
model. While these points have been well belabored before (Kvamme 1988a; Warren and
Asch 2000), a number of alternative performance statistics can greatly enhance
interpretation of various model qualities.
Our goal is the modeling of archaeological phenomena across space, yet our focus is
not on the archaeological site but on the location and whether or not a site is likely to be
present. (The location should be regarded as a point on the landscape.) Let event S signify
the actual presence of an archaeological site (or whatever archaeological phenomenon is
of interest) of a type we wish to model at a location. S′ then indicates the absence of such
a site at a location. An archaeological model can be regarded as a collection of irregular
polygons that are mapped onto the landscape that indicate locations that are “favorable,”
“likely,” or “probable” to contain an archaeological site of the type(s) being modeled. Let
M denote the event that a model, however derived, assigns a location as “likely” for the
site type of interest. M′ is its complement, meaning that the site type is unlikely according
to the model. M and M′ therefore represent the GIS mapping of model predictions, but it
must be discrete for this formulation. If a model mapping is continuous (as in a
probability surface) or ranked (e.g., polygons indicating variations in archaeological
likelihood), a GIS reclassification must be made at some threshold to achieve M and M′.
Models with continuous or ranked outcomes therefore have the advantage that statistics
may be generated under a variety of thresholds and graphed to yield richer and more
insightful performance indications (e.g., see Kvamme 1992; Warren and Asch 2000).
Most modelers focus on percent correct statistics for known archaeological site
classes, or 100 p(M|S) (the probability that a model specifies a site when one is known to
actually be present; the “|S” means “given” that a site is present). It is obtained simply by

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Everlasting Father, the Prince of Peace.” To us he is given, unto us he
is born.
I thought to have gone through what I designed on this subject,
but time will not allow. The Lord bless his word.
A DYING CHRISTIAN’S PRAYER.
“Receive my spirit,” was the prayer of Stephen to Jesus Christ, to
receive his departing soul; and, brethren, I think you will feel in a
dying hour, that your departing soul needs a Divine Saviour. You
have one in Jesus Christ. You may call upon him then, even as now.
His ear will not be heavy, though yours may, when death is sealing
up your faculties. His eye will not have lost its power of gazing
affectionately on you, when yours is becoming dim and closed. His
hand will not be shortened, in the hour when yours will have
become tremulous and feeble. But lift up the hand, the heart, the
eye, the soul, in prayer to him then, and you will find him a very
near and present help in that your time of trouble.
Brethren, a Christian should die praying. Other men die in
different ways, according to their character and temper. Julius Cesar
died adjusting his robes, that he might fall gracefully. Voltaire, with
mingled imprecations and supplications; Paine, with shrieks of
agonizing remorse. Multitudes die with sullenness, some with
blasphemies faltering on their tongue. But, brethren, the humble
Christian would die praying. Well says the poet:
“Prayer is the Christian’s vital breath,
The Christian’s native air;
His watch-word at the gates of death,
He enters heaven with prayer!”
But, observe for what Stephen prayed. “Lord Jesus receive my
spirit!” This is the prayer of faith, commending the immortal spirit to
the covenant care of Jesus. The spirit does not die with the body.

None but God, who gave, can take away the soul’s existence, and he
has declared that he never will. Would that bad men would think on
that! You cannot get rid of your soul’s existence: you cannot cease
to be: you may wish it; though the wish is monstrous and unnatural.
But there is no annihilation for any soul of man. Oh, come to our
Saviour! give him your guilty soul, to be justified through his
atonement, washed in his blood, regenerated by his Spirit. Make to
him now that surrender of your soul, for which he calls. Renew this
happy self-dedication every day, very especially every Sabbath, and
most solemnly, from time to time at the Lord’s Supper. And then,
when you come to die, it will only be, to do once more, what you
have so often done in former days,—again to commend your soul
very humbly, believingly, and affectionately, under the faithful care of
Jesus Christ.
THE HOUSE OF GOD.
The church was pleasantly situated on a rising bank, at the foot of
a considerable hill. It was surrounded by trees, and had a rural
retired appearance. In every direction the roads that led to this
house of God, possessed distinct but interesting features. One of
them ascended between several rural cottages from the sea-shore,
which adjoined the lower part of the village-street. Another winded
round the curved sides of the adjacent hill, and was adorned, both
above and below, with numerous sheep feeding on the herbage of
the down. A third road led to the church by a gently rising approach,
between high banks, covered with young trees, bushes, ivy, hedge-
plants, and wild flowers.—From a point of land, which commanded a
view of all these several avenues, I used sometimes, for a while, to
watch my congregation gradually assembling together at the hour of
Sabbath worship. They were in some directions visible for a
considerable distance. Gratifying associations of thought would form
in my mind, as I contemplated their approach and successive arrival
within the precincts of the house of prayer.—One day as I was thus

occupied, during a short interval previous to the hour of divine
service, I reflected on the joy, which David experienced at the time
he exclaimed, “I was glad when they said unto me, Let us go into
the house of the Lord. Our feet shall stand within thy gates, O
Jerusalem. Jerusalem is built as a city that is compact together;
whither the tribes go up, the tribes of the Lord, unto the testimony
of Israel, to give thanks unto the name of the Lord.” I was led to
reflect upon the various blessings, connected with the establishment
of public worship. “How many immortal souls are now gathering
together to perform the all-important work of prayer and praise—to
hear the word of God—to feed upon the bread of life! They are
leaving their respective dwellings, and will soon be united together
in the house of prayer.” How beautifully does this represent the
effect produced by the voice of the “Good Shepherd,” calling his
sheep from every part of the wilderness into his fold! As those fields,
hills, and lanes, are now covered with men, women, and children, in
various directions, drawing nearer to each other, and to the object of
their journey’s end; even so, “many shall come from the east, and
from the west, and from the north, and from the south, and shall sit
down in the kingdom of God.” Who can rightly appreciate the value
of such hours as these?—hours spent in learning the way of holy
pleasantness, and the paths of heavenly peace—hours devoted to
the service of God, and of souls; in warning the sinner to flee from
wrath to come; in teaching the ignorant how to live and die; in
preaching the gospel to the poor; in healing the broken-hearted; in
declaring “deliverance to the captives, and recovering of sight to the
blind.” “Blessed is the people that know the joyful sound; they shall
walk, O Lord, in the light of thy countenance. In thy name shall they
rejoice all the day, and in thy righteousness shall they be exalted.”
This train of reflection, at intervals, occurred powerfully to my
feelings, as I viewed that very congregation assembled together in
the house of God, whose steps, in their approach to it, I had
watched with prayerful emotions.—“Here the rich and poor met
together,” in mutual acknowledgement that “the Lord is the maker of
them all,” and that all are alike dependent creatures, looking up to
one common Father to supply their wants, both temporal and

spiritual.—Again, likewise, shall they meet together in the grave, that
undistinguishing receptacle of the opulent and the needy.—And once
more, at the judgment-seat of Christ, shall the rich and poor meet
together, that “every one may receive the things done in his body,
according to that he hath done, whether it be good or bad.” How
closely connected in the history of man, art these three periods of a
general meeting together. The house of prayer—the house appointed
for all living—and the house not made with hands eternal in the
heavens.—May we never separate these ideas from each other, but
retain them in a sacred and profitable union! So shall our
worshipping assemblies on earth be representative of the general
assembly and church of the first-born, which are written in heaven.
FINIS.

A CHOICE DROP OF HONEY
FROM
THE ROCK CHRIST;
OR,
A SHORT WORD OF ADVICE
TO
SAINTS AND SINNERS.
BY THOMAS WILCOCKS.
GLASGOW:
PRINTED FOR THE BOOKSELLERS.

CHRISTIAN READER,
I find, in this latter day, the love of the Lord shining in some
measure with its pleasant beams into my heart, warming my
affections, inflaming my soul not only to give a spiritual echo in soul
duty to so great a lover as my Saviour is, whose transcendent love
passeth knowledge, Eph. iii. 19. but also the loving and wishing well
to all Sion’s heaven-born children; for I find, in this day, many poor
souls tossed to and fro, ready to be carried away with every wind of
doctrine, by the sleight of men and cunning craftiness, whereby they
lie in wait to deceive, Eph. iv. 14: and that there are many
foundations to build upon that are false, upon which much labour is
spent in vain; that men are not speaking the truth in love; neither
are they growing up unto him in all things, which is the head Christ,
Eph. iv. 15. There cannot be a growing in Christ, without a union
with him. Thou wilt find, therefore, gentle reader, this ensuing little
treatise, if the Lord be pleased to bless the reading of it unto thee,
as a still voice behind thee saying, “This is the way, walk in it, that
thou turn not to the right hand or the left.”—The way into that
pleasant path of soul justification before God is in and through the
righteousness of Jesus Christ, for all our self-righteousness is as
filthy rags: surely shall one say, “In the Lord shall all the seed of
Israel be justified, and shall glory,” Isai. xlv. 25. It is only the dying
of that Just One, for us unjust ones, that must bring us to God. He
that knew no sin was made sin for us; that we who were nothing but
sin, might be made the righteousness of God in him, 2 Cor. v. 21.

Christian Reader, let all that is of old Adam in thee fall down at the
foot of Christ. He only must have the pre-eminence;—all the vessels
of this new spiritual covenant temple, from the cups to the flagons,
must be all hung upon Christ; he is to build the temple of the Lord,
and is to bear the glory; he, by his Father’s appointment, is the
foundation-stone, the corner-stone, and the top-stone; he is the
Father’s fulness of grace and glory: whatever thy wants be, thou
mayest come to him; there is balsam enough in him fit for a cure.
Reader, the good Lord help thee to experience the ensuing word
of advice, that it may be made by God unto thee like honey, sweet
to thy soul, and health to thy bones, and thy soul shall rejoice within
thee. Thy brother in the faith and fellowship of the gospel,
THOMAS WILCOCKS.

A CHOICE DROP OF HONEY
FROM THE
ROCK CHRIST.
A word of advice to my own heart and thine:—Thou art a professor,
and partakest of all ordinances: Thou dost well, they are glorious
privileges. But if thou hast not the blood of Christ at the root of thy
profession, it will wither, and prove but painted pageantry to go to
hell in.
If thou retain guilt and self-righteousness under it, those vipers
will eat out all the vitals of it at length.—Try and examine with the
greatest strictness every day, what foundation thy profession and thy
hope of glory is built upon, whether it was laid by the hand of Christ;
if not, it will never be able to endure the storm that will come
against it. Satan will throw it all down, and great will be the fall
thereof, Matt. vii. 27.
Glorious professor! thou shalt be winnowed, every vein of thy
profession shall be tried to purpose! It is terrible to have it all come
tumbling down, and to find nothing but it to rest upon.
Soaring professor! see to thy waxen wings betimes, which will
melt with the heat of temptations. What a misery it is, to trade
much, and break at length, and have no stock, no foundation laid for
eternity in thy soul!
Gilded professor! look if there be not a worm at the root, that will
spoil all thy fine gourd, and make it die about thee in a day of
scorching. Look over thy soul daily, and ask, “Where is the blood of

Christ to be seen upon my soul? What righteousness is it that I
stand upon to be saved? Have I got off my self-righteousness?”—
Many eminent professors have come at length to cry out in the sight
of the ruin of all their duties, Undone, undone, to all eternity!
Consider, the greatest sins may be hid under the greatest duties,
and the greatest terrors. See the wound that sin hath made in thy
soul be perfectly cured by the blood of Christ; not skinned over with
duties, humblings, enlargements, &c. Apply what thou wilt besides
the blood of Christ, it will poison the sore. Thou wilt find that sin was
never mortified truly; that thou hast not seen Christ bleeding for
thee upon the cross; nothing can kill it, but the beholding of Christ’s
righteousness.
Nature can afford no balsam fit for soul cure. Healing from duty
and not from Christ, is the most desperate disease. Poor ragged
nature, with all its highest improvements, can never spin a garment
fine enough, without spot, to cover the soul’s nakedness. Nothing
can fit the soul for that use, but Christ’s perfect righteousness.
Whatsoever is of nature’s spinning must be all unravelled, before
the righteousness of Christ can be put on; whatsoever is nature’s
putting on, Satan will come and plunder it every rag away, and leave
the soul naked and open to the wrath of God. All that nature can do
will never make up the least drachm of grace, that can mortify sin,
or look Christ in the face even for one day.
Thou art a professor, goest on hearing, praying, and receiving, yet
miserable thou mayest be. Look about thee; did thou ever yet see
Christ to this day in distinction from all other excellencies and
righteousness in the world, and all of them falling before the majesty
of his love and grace? Is. ii. 17.
If thou hast seen Christ truly, thou hast seen pure grace, pure
righteousness in him, every way infinite, far exceeding all sin and
misery. If thou hast seen Christ, thou canst trample upon all the
righteousness of men and angels, so as to bring thee into
acceptance with God. If thou hast seen Christ, thou wouldst not do a

duty without him for ten thousand worlds, 1 Cor. ii. 2. If ever thou
sawest Christ, thou sawest him a Rock, higher than self-
righteousness, Satan, and sin, Ps. lxi. 2; and this Rock doth follow
thee, 1 Cor. x. 4; and there will be continual dropping of honey and
grace out of that Rock to satisfy thee, Ps. lxxxi. 16. Examine if ever
thou hast beheld Christ as the only-begotten of the Father, full of
grace and truth, John, i. 14, 16, 17. Be sure thou art come to Christ,
that thou standest on the Rock of Ages, hast answered to his call to
thy soul, hast closed with him for justification.
Men talk bravely of believing, but whilst whole and sound few
know it. Christ is the mystery of the Scripture: Grace the mystery of
Christ. Believing is the most wonderful thing in the world. Put any
thing of thine own to it, and thou spoilest it; Christ will not so much
as look at it for believing. When thou believest and comest to Christ,
thou must leave behind thee thine own righteousness, and bring
nothing but thy sin. (O that is hard!) Leave behind thy holiness,
sanctification, duties, humblings, &c., and bring nothing but thy
wants and miseries, else Christ is not fit for thee, nor thou for Christ.
Christ will be a whole Redeemer and Mediator, and thou must be an
undone sinner, or Christ and thou will never agree. It is the hardest
thing to take Christ alone for righteousness: that is, to acknowledge
him Christ. Join any thing to him of thine own, and thou dost un-
Christ him.
Whatever comes in when thou goest to God for acceptance
besides Christ, call it anti-Christ bid it begone; make only Christ’s
righteousness triumphant; all besides that is Babylon, which must
fall if Christ stand; and thou shalt rejoice in the day of the fall
thereof, Is. xiv. 10, 11, 12.——Christ alone did tread the wine-press,
and there was none with him, Is. lxiii. 3. If thou join any thing to
Christ, Christ will trample upon it in fury and anger, and stain his
raiment with the blood thereof.——Thou thinkest it easy to believe;
was ever thy faith tried with an hour of temptation, or with a
thorough sight of sin? Was it ever put to wrestle with Satan, and the
wrath of God lying upon the conscience? When thou wast in the
mouth of hell and the grave, then God shewed thee Christ, a

ransom, a righteousness, &c. Then if thou couldst say, Oh, I see
grace enough in Christ, thou mayest say that which is the biggest
word in the world, Thou believest. Untried faith is uncertain faith.
To believing, there must go a clear conviction of sin, and the
merits of the blood of Christ, and of Christ’s willingness to save upon
this consideration merely, that thou art a sinner; things all harder
than to make a world. All the powers in nature cannot get up so
high in a storm of sin and guilt, as really to believe there is any
grace, any willingness, in Christ to save. When Satan charged sin
upon the conscience, then for the soul to bring it to Christ, that is
gospel-like. That is to make him Christ, he serves for that use. To
accept Christ’s righteousness alone, his blood alone, for salvation,
that is the sum of the gospel. When the soul, in all duties and
distresses, can say, Nothing but Christ, Christ alone for
righteousness, justification, sanctification, redemption, 1 Cor. i. 30;
not humblings, nor duties, nor graces, &c., that soul hath got above
the reach of the billows.
All temptations, Satan’s advantages, our complainings, are laid in
self-righteousness, and self-excellency: God pursueth these, by
setting Satan upon thee, as Laban did Jacob for his images; these
must be torn from thee, he is unwilling as thou wilt; these hinder
Christ from coming in; and till Christ come in, guilt will not come
out; and where guilt is, there is hardness of heart; and therefore
much guilt argues little if any thing of Christ.
When guilt is raised up, take heed of getting it allayed any way
but by Christ’s blood, that will tend to hardening. Make Christ thy
peace, Eph. i. 14, not thy duties, thy tears, &c. Thou mayest offend
Christ by duties as well as sins. Look at Christ, and do as much as
thou wilt. Rest with all thy weight upon Christ’s righteousness; take
heed of having one foot on thine own righteousness and another on
Christ’s. Till he come and sit on high, upon a throne of grace in the
conscience, there is nothing but guilt, terror, secret suspicions, the
soul hanging betwixt hope and fear, which is an un-gospel-like state.

He that fears to see sin’s utmost vileness, the utmost hell of his
own heart, suspects the merits of Christ. Be thou never such a great
sinner, 1 John, ii. 1; try Christ, to make him thy advocate, and thou
shalt find him Jesus Christ the righteous. In all doubtings, fears,
storms of conscience, look at Christ continually. Do not argue it with
Satan, he desires no better. Bid him go to Christ, and he will answer
him. It is his office to be our advocate, 1 John, ii. 1. His office is to
answer the law as our surety, Heb. vii. 22; his office to answer
justice, as our Mediator, Gal. iii. 20; 1 Tim. ii. 5. And he is sworn to
that office, Heb. vii. 20, 21. Put Christ upon it. If thou wilt do any
thing thyself to satisfaction for sin, thou renouncest Christ the
righteous, who was made sin for thee, 2 Cor. v. 21.
Satan may alledge, and corrupt scripture, but he cannot answer
scripture. It is Christ’s word of mighty authority. Christ foiled Satan
with it, Matt. iv. 10. In all the scripture there is not an ill word
against a poor sinner stripped of self-righteousness; nay, it plainly
points out this man to be the subject of the grace of the gospel, and
none else. Believe but in Christ’s willingness, and that will make thee
willing. If thou findest thou canst not believe, put him upon it; he
works to will and to believe, put him upon it; he works to will and to
do of his own pleasure, Phil. ii. 13. Mourn for thy unbelief, which is a
setting up of guilt in the conscience above Christ, an undervaluing of
the merits of Christ, accounting his blood an unholy, a common, and
unsatisfying thing.
Thou complainest much of thyself.—Doth thy sin make thee look
more at Christ, less at thyself! That is right, else complaining is but
hypocrisy. To be looking at duties, graces, enlargements, when thou
shouldst be looking at Christ, that is pitiful. Looking at them will
make you humble. By grace ye are saved, Eph. ii. 5, 8. In all thy
temptations be not discouraged, James, i. 2. Those surges may be
not to drown thee, but to cast thee on the Rock Christ.
Thou mayest be brought low, even to the brink of hell, yet there
thou mayest cry, there thou mayest look towards the holy temple,
Jonah, ii. 14. Into that temple none might enter but purified ones,

and with an offering too, Acts, xxi. 26. But now Christ is our temple,
sacrifice, altar, and high-priest to whom none must come but
sinners, and that without any offering but his own blood once
offered. Heb. vii. 27.
Remember all the patterns of grace that are in heaven. Thou
thinkest, “Oh what a monument of grace shall I be!” There are many
thousands as rich monuments as thou canst be. The greatest sinner
did never surpass the grace of Christ. Do not despair: hope still.
When the clouds are blackest, even then look towards Christ, the
standing pillar of the Father’s love and grace, set up in heaven, for
all sinners to gaze upon continually. Whatsoever Satan or conscience
say, do not conclude against thyself. Christ shall have the last word;
he is judge of quick and dead, and must pronounce the fatal
sentence. His blood speaks reconciliation, Col. i. 20; cleansing, 1
John, i. 7; purchase, Acts xx. 28; redemption, 1 Pet. i. 9; purging,
Heb. v. 13, 14; remission, verse 22; liberty, Heb. x. 19; justification,
Rom. v. 9; nearness to God, Eph. ii. 13. Not a drop of this blood shall
be lost. Stand and hearken what God will say, for he will speak
peace to his people, that they return no more to folly, Psal. lxxxv. 8.
He speaks grace, mercy, and peace, 2 Tim. i. 2. That is the language
of the Father and of Christ. Wait for Christ’s appearing, as the
morning star, Rev. xxii. 19. He shall come as certain as the morning,
as refreshing as the rain, Hos. vi. 3.
The sun may as well be hindered from rising, as Christ the sun of
righteousness, Mal. iv. 2. Look not a moment off Christ. Look not
upon sin, but look upon Christ first: when thou mournest for sin, if
thou dost not see Christ, then away with it, Zech. ii. 20. In every
duty look at Christ; before duty, to pardon; in duty, to assist; after
duty, to accept. Without this it is but carnal careless duty. Do not
legalise the gospel, as if part did remain to thee to do and suffer,
and Christ were but an half mediator; and thou must bear part of
thine own sin, and make part satisfaction. Let sin break thy heart,
but not thy hope in the gospel.

Look more at justification than sanctification. In the highest
commands consider Christ, not as an exactor, to inquire, but a
debtor and undertaker, to work. If thou hast looked at workings,
duties, qualifications, &c., more than at the merits of Christ, it will
cost thee dear; no wonder thou goest complaining; graces may be
evidences, the merits of Christ alone, without them, must be the
foundation of thy hope to rest upon. Christ only can be the hope of
glory, Col. i. 27.
When we come to God, we must bring nothing but Christ with us.
Any ingredients, or any previous qualifications of our own, will
poison and corrupt faith. He that builds upon duties, graces, &c.,
knows not the merits of Christ; this makes believing so hard, so far
from nature. If thou believest, thou must every day renounce as
dung and dross, (Phil. iii. 7, 9,) thy privileges, thy qualifications, thy
baptism, thy sanctification, thy duties, thy graces, thy tears, thy
meltings, thy humblings, and nothing but Christ must be held up.
Every day thy workings, thy self-sufficiency must be destroyed. Thou
must take all out of God’s hand. Christ is the gift of God, John, iv.
10. Faith is the gift of God, Eph. ii. 1. Pardon a free gift, Rom. v. 16.
Ah, how nature storms, frets, rages at this, that all is of gift, and it
can purchase nothing with its actings, and tears, and duties; that all
workings are excluded, and of no value in heaven!
If nature had been to contrive the way of salvation, it would rather
have put it into the hands of saints or angels to sell it, than the
hands of Christ, who gives freely, whom therefore it suspects; nature
would have set up a way to purchase by doing; therefore it
abominates the merits of Christ, as the most destructive thing to it.
Nature would do any thing to be saved, rather than go to Christ, or
close with Christ, and owe all to him. Christ will have nothing; but
the soul will force somewhat of his own upon Christ. Herein is that
great controversy.—Consider—didst thou ever yet see the merits of
Christ, and the infinite satisfaction made by his death? Didst thou
see this when the burden of sin and the wrath of God lay heavy on
thy conscience? That is grace. The greatness of Christ’s merit is not

known but to a poor soul in deep distress! Slight convictions will but
have slight low prizings of Christ’s blood and merits.
Despairing sinner! Thou lookest on thy right hand, and on thy left,
saying, “Who will shew us any good?” Thou art looking over all thy
duties and professions to patch a righteousness to save thee. Look
at Christ now; look to him and be saved all the ends of the earth, Is.
xlv. 22. There is none else. He is a Saviour, and there is none
besides him, xliii. 11. Look any where else, and thou art undone.
God will look at nothing but Christ, and thou must look at nothing
else. Christ is lifted up on high, as the brazen serpent in the
wilderness, that sinners at the end of the earth, at the greatest
distance, may see him, and look towards him, John, iii. 14, 15. The
least sight of him will be saving, the least touch healing to thee; and
God intends thou shouldst look on him, for he hath set him upon a
high throne of glory, in the open view of all poor sinners. Thou hast
infinite reason to look on him: no reason at all to look off him; for he
is meek and lowly of heart, Matt. xi. 29. He will do that himself
which he requires of his creatures; viz. bear with infirmities, Rom.
xv. 1. Not pleasing himself, nor standing upon points of law, ver. 2;
he will restore with the spirit of meekness, Gal. vi.; and bear thy
burdens, ver. 2. He will forgive not only till seven times, but seventy
times seven, Matt. xviii. 21, 22. I put the faith of the apostles to it to
believe this, Luke, xvii. 4, 5. Because we are hard to forgive, we
think Christ is hard.
We see sin great, we think Christ doth so, and measure infinite
love with our line, infinite merits with our sins, which is the great
pride and blasphemy, Ps. ciii. 11, 12; Is. x. 15. Hear what he saith: I
have found a ransom, Job xxxiii. 24; in him I am well pleased, Matt.
iii. 18. God will have nothing else; nothing else will do thee good, or
satisfy conscience, but Christ who satisfied the Father. God doth all
upon the account of Christ. Thy deserts are hell, wrath, rejection.
Christ’s deserts are life, pardon, and acceptance. He will not only
shew thee one, but he will give thee the other. It is Christ’s own
glory and happiness to pardon. Consider, whilst Christ was upon the
earth, he was more among publicans and sinners, than among

scribes and pharisees, his professed adversaries, for they were
righteous ones: it is not as thou imaginest, that his state in glory
makes him neglected, scornful to poor sinners; No. He hath the
same heart now in heaven; he is good, and changeth not; he is the
Lamb of God that taketh away the sins of the world, John, i. 20. He
went through all thy temptations, dejections, sorrows, desertions,
rejections, Matt. iv. 3 to 12 and 26; Mark, xv. 24; Luke, xxii. 44;
Matt. xxiv. 38. And he hath drawn the bitterness of the cup, and left
thee the sweet: the condemnation is out; Christ drank up all the
Father’s wrath at one draught, and nothing but salvation is left for
thee. Thou sayest thou canst not believe, thou canst not repent.
Fitter for Christ if thou hast nothing but sin and misery. Go to Christ
with all thy impenitence and unbelief, to get faith and repentance
from him—that is glorious: Say unto him, Lord, I have brought no
righteousness of grace to be accepted in or justified by; I am come
for thine. We would be bringing to Christ, which must not be; grace
will not stand with works, Tit. iii. 5; Rom. xi. 6. Self-righteousness
and self-sufficiency are the darlings of nature, which she preserves
as her life; that makes Christ obnoxious to nature; nature cannot
desire him; he is just directly opposite to all nature’s glorious
interests. Let nature make a gospel, and it would make it contrary to
Christ. It would be to the just, the innocent, the holy, &c. Christ
made the gospel for thee, that is, for needy sinners, the ungodly, the
unrighteous, the accursed. Nature cannot endure to think the gospel
is only for sinners; it will rather choose to despair than go to Christ
upon such terrible terms. When nature is opposed to guilt or wrath,
it will go to its own haunts of self-righteousness, self-goodness, &c.
An infinite power must cast down those strong holds. None but the
self-justiciary stands excluded out of the gospel. Christ will look at
the most abominable sinner before him, because to such a one
Christ cannot be made justification—he is no sinner. To say in
compliment, I am a sinner, is easy; but to pray with the publican
indeed, Lord be merciful to me a sinner, is the hardest prayer in the
world. It is easy to profess Christ with the mouth, but to confess him
with the heart, as Peter, (to be the Christ, the Son of the living God,
the alone Mediator,) that is above flesh and blood. Many call Christ

Saviour; few know him to be so. To see grace and salvation in Christ,
is the greatest sight in the world; none can do that, but at the same
time they shall see that glory and salvation to be theirs. I may be
ashamed to think, in the midst of so much profession, that I have
little of the blood of Christ, which is the main thing of the gospel. A
Christless formal profession will be the blackest sight next to hell.
Thou mayest have many good things, and yet one thing may be
wanting that may make thee go away sorrowful from Christ. Thou
hast never sold all thou hast, never parted with all thine own
righteousness, &c. Thou mayest be high in duty, and yet a perfect
enemy and adversary to Christ, in every prayer, in every ordinance.
Labour after sanctification to thy utmost, but make not a Christ of
it to save thee; if so, it must come down one way or other.
Christ’s infinite satisfaction, not thy sanctification, must be thy
justification before God. When the Lord shall appear terrible out of
his holy place, fire shall consume that as hay and stubble. This will
be found true religion, to rest all upon the everlasting mountains of
God’s love and grace in Christ; to live continually in the sight of
Christ’s infinite righteousness and merits, (they are sanctifying;
without them the heart is carnal,) and in those sights to see the full
vileness of sin, and to see all pardoned; in those sights to pray, hear,
&c., seeing thy polluted self, and all thy weak performances accepted
continually; in those sights to trample upon all thy self-glories,
righteousness, and privileges, as abominable, and be found
continually in the righteousness of Christ only; rejoicing in the ruins
of thy own righteousness, the spoiling of all thy own excellencies,
that Christ’s alone, as Mediator, may be exalted on his throne:
mourning over all thy duties (how glorious soever) which thou hast
not performed in the sight and sense of Christ’s love. Without the
blood of Christ on the conscience, all this is dead service, Heb. ix.
14.
That opinion of free will, so cried up, will be easily confuted, as it
is by scripture, in the heart that hath had any spiritual dealings with
Jesus Christ, as to the application to its merit, and subjection to his

righteousness. Christ is every way too magnificent a person for a
poor nature to close withal or to apprehend. Christ is so infinitely
holy, nature durst never look at him; so infinitely good, nature can
never believe him to be such, when it lies under a full sight of sin.
Christ is too high and glorious for nature so much as to touch. There
must be a divine nature first put in the soul, to make it lie on him,
he lies so infinitely beyond the sight or reach of nature.
That Christ, which natural free will can apprehend, is but a natural
Christ of a man’s own making, not the Father’s Christ, nor Jesus the
Son of the living God, to whom none can come without the father’s
drawing, John, vi. 44. 46. Finally, search the scriptures daily, as
mines of gold, wherein the heart of Christ is laid. Watch against
constitutional sins, see them in their vileness, and they shall never
break out into act. Keep always an humble, empty, broken frame of
heart, sensible of any spiritual miscarriage, observant of all inward
workings, fit for the highest communications. Keep not guilt in the
conscience, but apply the blood of Christ immediately. God chargeth
sin and guilt upon thee, to make thee look to Christ.
Judge not Christ’s love by providences, but by promises. Bless God
for shaking off false foundations, and for any way whereby he keeps
the soul awakened and looking after Christ. Better sicknesses and
temptations than security and slightness.
A slighting spirit will turn a profane spirit, and will sin and pray
too. Slighting is the bane of profession; if it be not rooted out of the
heart, by constant and serious dealings with, and beholdings of
Christ in duties, it will grow more strong and more deadly by being
under church ordinances. Measure not thy graces by other
attainments, but by Scripture trials. Be serious and exact in duty,
having the weight of it upon the heart; be as much afraid of taking
comfort from duties as from sins. Comfort from any hand but Christ’s
is deadly. Be much in prayer, or you will never keep up much
communion with God. As you are in closet prayer, so you will be in
all other ordinances.

Reckon not duties by high expression, but by low frames, and the
beholdings of Christ. Tremble at duties and gifts. It was a saying of a
great saint, he was more afraid of his duties than his sins; the one
often made him proud, the other always made him humble. Treasure
up manifestations of Christ’s love, they make the heart low for
Christ, too high for sin. Slight not the lowest, meanest evidences of
grace; God may put thee to make use of the lowest as thou thinkest,
even that, 1 John, iii. 14, may be worth a thousand worlds to thee.
Be true to truth, but not turbulent and scornful. Restore such as
are fallen; help them up again with all the bowels of Christ. Set the
broken disjointed bones with the grace of the gospel. High professor,
despise not weak saints. Thou mayest come to wish to be in the
condition of the meanest of them. Be faithful to others’ infirmities,
but sensible of thy own. Visit sick beds and deserted souls much,
they are excellent schools in experience. Abide in your calling. Be
dutiful to all relations as to the Lord. Be content with little of the
world; little will serve. Think every little of the earth much, because
unworthy of the least. Think much of heaven, not little, because
Christ is so rich and free. Think every one better than thyself, and
ever carry self-loathing about thee, as one fit to be trampled upon
by all saints. See the vanity of the world, and the consumption there
is upon all things, and love nothing but Christ. Mourn to see so little
of Christ in the world, so few needing him: trifles please them better.
To a secure soul Christ is but a table, the scripture but a story.
Mourn to think how many there are under baptism and church order,
that are not under grace, looking much after outward duties, little
after Christ, little versed in grace. Prepare for the cross; welcome it,
bear it triumphantly like Christ’s cross; whether scoffs, mockings,
jeers, contempt, imprisonment, &c. But see it be Christ’s cross, not
thine own.
Sin will hinder from glorying in the cross of Christ. Omitting little
truths against light may breed guilt in the conscience, as well as
committing the greatest sins against light. If thou hast been taken
out of the belly of hell into Christ’s bosom, and made to sit among
princes in the household of God, oh how shouldst thou live as a

pattern of mercy? Redeemed, restored soul, what infinite sums dost
thou not owe to Christ! With what singular frames must thou walk,
and do every duty! On sabbaths, what praising days, singing
hallelujahs, should they be to thee! Church fellowship: what a
heaven, a being with Christ, and angels, and saints in communion;
what a bathing of the soul in eternal love; what a burial with Christ,
and dying to all things beside him! Every time thou thinkest of
Christ, be astonished, and wonder; and when thou seest sin, look at
Christ’s grace which did pardon it; and when thou art proud, look at
Christ’s grace, that shall humble and strike thee down in the dust.
Remember Christ’s time of love, when thou wast naked, Ezekiel,
xvi. 8, 9, and then he chose thee. Canst thou ever have a proud
thought?—Remember whose arms supported thee from sinking, and
delivered thee from the lowest hell, Ps. lxxxvi. 13: and shout in the
ears of angels and men, Ps. cxlviii. and for ever sing, “Praise, praise,
grace, grace.” Daily repent and pray; and walk in the spirit of grace
as one that hath the anointing of grace upon thee. Remember thy
sins, Christ’s pardoning; thy deserts, Christ’s merits; thy weakness,
Christ’s strength; thy pride, Christ’s humility; thy many infirmities,
Christ’s restorings; thy guilt, Christ’s new applications of his blood;
thy failings, Christ’s raisings up; thy wants, Christ’s fulness; thy
temptations, Christ’s tenderness; thy vileness, Christ’s righteousness.
Blessed soul! whom Christ shall find not trusting in his own
righteousness, Phil. iii. 9, but having his robes washed and made
white in the blood of the Lamb, Rev. vii. 14. Woeful, miserable
professor, that hath not the gospel within! Rest not in church trials;
thou mayest pass them, and be cast away in Christ’s day of trial.
Thou mayest come to baptism, and never come to Jesus and the
blood of sprinkling, Heb. xii. 24. Whatever working or attainments,
short of Christ s blood, merits, righteousness, (the main object of
the gospel) fall short of the truth, and leave the soul in a condition
of doubtings and questionings; and doubtings, if not looked into
betimes, will turn to a lightness of spirit, one of the most dangerous
of frames.

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