2. sem exploratory factor analysis copy (2)
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This document provides an overview of factor analysis, including its purposes, key steps, and assumptions. Factor analysis is used to reduce a large set of variables into a smaller set of underlying factors or dimensions while preserving as much of the original information as possible. The main steps are designing the analysis, selecting variables, ensuring sufficient sample size, checking assumptions, extracting factors, interpreting the results, and rotating factors to aid interpretation. The goal is to identify the fundamental constructs or dimensions that explain relationships among variables.
2. sem exploratory factor analysis copy (2)
- 1. FACTOR ANALYSIS 1. Dimension Reduction: 80 characteristics of retail shops and their services what consumers wanted to be changed. The owner wants to reduce them into fewer dimensions. The consultant collected data from consumers and then did factor analysis. 2. Variable Reduction: On the basis of grouping variables, 20 variables 3 factors may emerge. 3. Test Items into Factors: Twenty items proposed to measure ethical leadership in our study reduced into two factors- empowerment, motive and character. The general purpose of FA is to find out a way of condensing /summarizing the information contained in a number of original variables into a smaller set of new, composite dimensions or factors with a minimum loss of information –that is, to search for and define the fundamental constructs or dimensions assumed to underlie the original variables. 1. Identify the structure of relationship among variables or respondents. R FA analyses a set of variables to identify the dimensions that are latent. Q FA analyses a large no individuals into distinct groups. 2. Identify the representative variables. 3. Create a new set of variables much smaller in number for subsequent analysis. Stage 2: Designing a FA Correlation Among Variables (R)/ Respondents (Q). Correlation matrix. Q FA (similarity of individuals on variance structure) and Cluster analysis (distance among respondents scores). Variable Selection and Measurement Issues Metric measurement of variables and some variables may be nonmetric or dummy. If all variables are dummy, then Boolean FA. Reasonable number of variables per factor, generally five or more. Sample Size Needs to be > 100 or larger. 5 or 10 times observations X number of variables to be analysed. If there are 30 items in a scale, there needs to be 1
- 2. 150 or 300 respondents to apply FA. Cases per Variable= 5 or 10 minimum. More cases will minimize the over fitting to the data. Stage 3: Assumptions in FA Correlation in substantial number of cases is >.30, or partial correlation low. DV, IV mixed in FA is inadequate. Male and female mixed. Separate analysis for each group FA. Stage 4: Deriving Factors and Assessing Overall Fit Method of extracting factors (common factor analysis vs. component analysis/principal component analysis) and number of factors selected to represent the underlying structure in the data. Common factor analysis extract factors specifying what the variables share in common. Component analysis/principal component analysis specifies the minimum number of factors. Total Variance= Common + specific + error Criteria for the Number of Factors to be Extracted 1. Latent root criterion 2. A priori criterion; Percentage of variance extracted =60%, Scree test criterion, latent root :1 Stage 5: Interpreting Factors Factor loadings are correlation of each variable and the factor. Factor rotation: for interpretation. The reference axis of the factors are turned about the origin until some other position has been reached. Orthogonal 900 Insert Figure Criterion for Significance of Loadings 350= .30, 250=. 35, 200=.40, 150=. 45, 100=.55, 85=.60, etc. 2