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Unformatted text preview: Confirmatory Factor Analysis: Evaluation Psychology 588: Covariance structure and factor models Feb 24, 2010 Evaluating a model is equivalent to testing a hypothesis of a set of constraints (that make whether explicit or implicit), provided that all other assumptions fulfilled  similar to the logic behind null hypothesis testing All overall fits quantify whether they are statistical or standardized (i.e., bounded by [0,1]) Overall fit indicates goodness (or badness) of the whole model, summarizing into a scalar value Individual fits tell goodness of fit to particular manifest DVs (as indicated by R 2 or SMC) and standard error of parameters indicate how reliable parameter estimates are  both overall and individual fits should be evaluated! Evaluation 2 , S S S Residuals indicate how the specified model predicts individual covariances  note that the variances s ii have no residual in recursive models Sources of residuals: ( ), which we want to know by the residuals sampling fluctuation  with large N , smaller residuals are expected if the model is correct ** scale of observed variables determines the size of residuals  if correlations are analyzed, residuals would not have scale dependency, varying [2,2] Residuals 3 ij ij s RMR (root meansquare of residual) 4 Note that the denominator counts variances as well As an alternative to residuals, fit to covariances may be compared by normalized residuals (useful to spot where the model predict poorly): ( ) ( ) 1/2 2 1, 1 RMR 2 1 q i ij ij i i j j s q q = = = + ( ) ( ) ( ) 1/2 1/2 2 N.R. residual avar residual ij ij ii jj ij s N = = + RMR represents average residual, as SD indicates an average deviation of a variable around its mean Chisquare test (Browne, 74, 82, 84) 5 The most common parametric statistical test for overall fit...
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This note was uploaded on 06/11/2010 for the course PSYC 588 taught by Professor Sunjinghong during the Spring '10 term at University of Illinois at Urbana–Champaign.
 Spring '10
 SunjingHong
 Psychology

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