Geospatial Thinking - MCA foundations
I think it is fair to say that GIS was made for Multi-Criteria Analysis (MCA). the very idea of layers of data implies that GIS and MCA are ideal bed fellows.
MCA really started in the non-spatial world of decision making. Usually you would be talking about some kind of tabular analysis of options using a set of scored and weighted criteria. MCAS's in this context are not that conceptually complicated and have a general objective of providing a logical framework for decision making. In this tabular space the critical precursor to the decision making is working out what the assessment criteria and metrics are.
Tip: when developing criteria - "less means you know more"
I have seen criteria lists that run to 50 to 60 items. This tells you that we don't really know what problem we are solving and or we are comparing apples with oranges, more on this later. Fun fact - the human brain can only consistently compare about 5 to 7 things at any one time. Translating MCA into a spatial context seems like a simple and straightforward idea - on the surface! However there are a few things I think worth thinking about if your on a MCA journey. The following is a set of consideration I used when undertaking spatial MCA. I have posed each as a question.
Consideration: what is your analytical framework?
Anyone who has worked with me on a problem knows I love like to start with a framework for thinking and acting. In the case on MCA's this falls nicely into my Spatial Logic Framework. The image blow illustrates the 5 steps in this process. I am not going to dwell too much on this other than to say there is great value in a consist framework in geospatial analysis is obvious but often overlooked. A framework for thinking about a problem gives the foundation for efficiency and ensures you are not forgetting any of the fundamentals.
Consideration: have you considered the 3R of MCA's?
When embarking on an MCA I always think about the 3 R’s. This ensures I have not forgotten anything important. The 3 R’s are not independent – decision in one effect the others. So what are the 3 R's?
Representation – Information is represented in MCAs as Criteria/Metric combinations. Criteria must be defined clearly. Part of that definition is the information that will be used to represent said criteria. Each criteria is represented as a metric of some kind. Any MCAs that use scoring as a metric needs a standardised scoring methodology.
Resolution – What is the “scale” of my analysis? What is the biggest / smallest geographic unit that I can say anything meaningful about in this study? What type of geography makes sense for this study? What is the scale of reporting? What unist an I using? How do they relate to the analysis geography?
Relationship – This is how you go about creating individual criteria (what you do to create a criterion/metric from your available data), how the criteria relate to each other and any issues of relative significance (weighting). Relationship is also about what method you will use to combine your criteria (what algorithm makes sense for your criteria). the most common MCA algorithm is weighted sum. This is a choice not a rule.
Consideration: what is my topology of MCA concepts?
You have done the thinking ala the 3R's.. Great! What I like to do next is revisit my MCA topology as a way to ensure I am getting all the info I need from my stakeholder well before we start mucking about with data. At this point I am really asking - do we know enough about the problem to proceed.
Consideration: what questions are we asking, and when?
Analysis is all about questions, geospatial analysis is no exception. I like to frame core questions in a sequence. Keep in mind questions follow questions - there is often an order.
Consideration: what can I exclude up front?
It's good practice to ask your stakeholder the following questions.
Doing this removes noise from you analysis. This can simplify the process and keep you focused on areas that actually matter. I call these exclusion zones.
TIP: The definition of Exclusion Zones should be treated in the same ways as other criteria. Exclusion criteria need clear documented definitions. Trust me, when you're asked why you excluded spaces from you analysis you will be glad that you did this step.
Consideration: do you have to many criteria?
You will recall I mention the humans can only juggle 5-7 things at a time. It's even less when they are very different ideas. For example what does it mean to compare rare planta with the cost of a roads? What it usually means is you asking the wrong question.
When there are a lot of criteria in a study it usually follows that those criteria can be grouped. A common grouping is the triple bottom line. The purpose of grouping is to define a hierarchy of questions. For example, when you score/weight within a group you will do so with question focused on that group - for example "what is the relative importance of these environmental criteria?". When you score/weight between groups you will be asking a different question - usually something like "how does group X influence the decision compared to group Y".
Consideration: do you know why where matters?
Many MCAs produce a heatmap as the result of the combination of criteria. The heatmap tells you where there are high or low values to the question that your MCA is addressing. The Heatmap does not tell you why they are high or low. Consider that two locations can have the same heatmap “value” but may have got that result for different reasons, that is, different combinations of criteria (profiles) can result in the same MCA “answer”. The profile of the inputs to your heatmap tells you why a location is high or low.
From a decision-making perspective where action is required is defined by the heatmap (where) but what management actions needed are defined by the criteria profile (why).
Consideration: just adding things up - really?
Let's switch focus to how you implement a MCA. Lots of folks take for granted it's a weighted sum algorithm. There is nothing at all that suggests this has to be the case. It is however very common way to implement a MCA. The key question is not what method is appropriate but rather what does it mean to implement MCA in a particular way.
Let's illustrate this with a simple example.
Imagine we have a two criteria MCA problem. Road Density (quantity of road network per unit area) and River Density (quantity of rivers per unit area). The usual thing would be to classify these into your scoring zones (in this case let's assume 1,2 and 3 (low, medium and high). The next step would be to do a weighted sum (more on that later) to get your heat map or MCA result..
This raises a few questions:
The problem we face is illustrated in the diagrams below.
So which is the right way? That really depends on the aim of the MCA. In practice I like to use both wherever I can. The heat map (weighted sum) gives use the WHERE the unique combination of criteria other describes the WHY. I find both useful when it comes to using the geospatial outputs for decision-making. The image below is a summary of the issue. Clearly this gets more complex as you add more criteria to the mix.
Consideration: are you clear what your cost curve is?
In most MCA exercises we spend significant time defining criteria and scoring regimes. One of the most popular scoring regimes is a 5 class regime that goes from Very Low through Medium to Very High – this is represented by classes (1,2,3,4,5). The question here is not what is 1 or 5 but what the difference between 1 and 5 represents – in economics this is called a cost curve. It describes the “rate of change” between the classes.
In the table below we have an example of three cost curves for the same 5 class regime. Linear-L (probably the most common), Order of Magnitude-O and Exponential-E – there are any number of ways to define a cost curve. What’s important is that you think about what the class difference represents and have a logical regime in place to define and implement it.
The graphs below shows the cost curves plotted – as you can see very different results. In the Linear case (the least severe) there is very little difference (4 units) while in the Order of Magnitude case (most severe) there are 10,000 units.
In an MCA this can impact the results quite a bit! This is particularly the case when the final MCA combined cost surface is used in geospatial operations like least-cost path (LCP) analysis. The reason it matters in the LCP is because the function considers the overall distance between start and end and is always gravitating towards a straight line. So if your cost surface has very little difference (linear) then don't be surprised if the LCP is more or less a straight line, especially over long distances.
To illustrate this a simple example below of a 5x5 grid (x,y in the table) a a cost value (z) using the three types of cost curve above applied to random integers between 1 and 5. So the take home here is.. know your cost curve.
Consideration: do you remember I mention more is less wrt criteria?
This is about minimising the number of criteria to just those that will affect the decision. I thought I would revisit this as the final consideration we will look at in this article.
In MCA's it's tempting just to add more and more criteria to accommodate all the competing views. A way to think about this is that each criterion represents a component of a decision landscape. The job of the analyst is to create a clear and consistent model of that landscape. Getting all the cards (criteria) on the table is worth dong initially just to get a feel for stakeholder issues, competing views and help in developing a clear decision landscape. However you will, at some point need to make sense of it all.
Let's do another thought experiment. Imaging you had three MCA with the following number of classes 10, 20 and 30 criteria.
It's important to realise that MCA’s are a zero sum game. Why? Strictly speaking weighting in whatever form you do it is relative to a whole. That is, adding more criteria only splits the pie more it does not make the pie bigger. So what is the implication of this? The core question is... How Significant is an individual criterion to the result?
The experiment is shown below – the rule here is the more criteria involved the more each individual criterion tends to having less influence on the result.
So what can you do about this issue if you need to do a MCA? One avenue is to “Group” the criteria up. What is a Group? A Group is a sub-set of criteria that address the core question of the MCA from a similar perspective. A Common set of Groups in MCA is the Triple Bottom Line – Eco monic, Social, Environmental - TBL. Groups also helps with another issues:
Here is a example, assume:
The concept of group is show below. The take home here is to know what questions are driving your decision landscape!
There are other considerations like:
These are for another time. If you can think of other considerations feel free to drop a comment.
My final comment on MCA's is don't just go through the motions. Think, understand and communicate the assumptions and consequences of the decision making landscape you are creating.