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#### Appendix A: Additional Information about Factor Analysis and Cluster Analysis Pages 103-112

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 From page 103...... The following pages explain latent variables, FA and related methods, cluster analysis, and structural equation modeling. LATENT VARIABLES Latent variables are variables that are not measured directly but are measured indirectly by using observed variables. Read the entire page → From page 104...... Rather than entering individual response data, the analyst may enter the intercorrelation matrix itself. Table A.1 shows a hypothetical intercorrelation matrix for a dataset that included responses to six items. Read the entire page → From page 105...... Factor Extraction One distinction among FA methods is the statistical approach used in "factor extraction." Two of the available choices are reviewed, common FA and principal component analysis (PCA) Read the entire page → From page 106...... The two models will be nested, and their fit can be compared via a likelihood ratio test or chi-squared difference test to determine whether the constrained model fits significantly worse. If so, measurement invariance cannot be claimed. Read the entire page → From page 107...... For example, if there were both neurologic and respiratory variants of CMI, one would expect a three-class model with one class of relatively asymptomatic people, a second class with high conditional probabilities of the neurologic symptoms but low probabilities of other symptoms, and a third class with high conditional probabilities of the respiratory symptoms but low probabilities of other symptoms. Like FA, LCA entails assumptions of independent people and local independence. Read the entire page → From page 108...... Confirmation of the latent class model would entail replicating both the number of classes and the conditional probability estimates for each class. A formal test of measurement invariance would entail fitting the latent class model in two separate samples. Read the entire page → From page 109...... Cluster analysis is not a latent-variable method; it does not assume that an underlying latent variable accounts for any associations between observed variables. Instead, cluster analysis is a type of computational learning method that aims to find clusters that are not known in advance. Read the entire page → From page 110...... Structural-equation models can be used to model associations with latent variables. In those models, associations are estimated jointly with the measurement model (such as the factor analysis or latent class analysis) Read the entire page → From page 111...... 1990. Component analysis versus common factor analysis: Some issues in selecting appropriate procedures. Read the entire page → From page 112...... 2006. Scale development research: A content analysis and recommendations for best practices. Read the entire page →

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