lecture10_s10 CFA - Confirmatory Factor Analysis Model...

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Confirmatory Factor Analysis: Model comparison, respecification, and more Psychology 588: Covariance structure and factor models Feb 26, 2010
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Model comparison 2 • Essentially all goodness of fit indices are descriptive, with no statistical device for selecting from alternative models (see table 7.8, p. 290 for the political democracy example) • Same for other types of fits (e.g., AIC, BIC) or cross-validation technique • Chi-square difference test available for comparing a nested model with a nesting model, provided that all assumptions are met and more importantly the nesting model is correct • Why does a nested model must produce an equal or higher chi- square value regardless of types of constraints (e.g., constant, equality, or any functional form)? Impossible at all to have a lower value?
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Likelihood ratio test for ML 3 F LR itself is a chi-square variable with df = df nested df nesting • Null hypothesis --- a set of constraints (as the only difference between the nested and the nesting model) hold in the population F LR is conditional to the nesting model --- consequence of an additional constraint will depend on what’s already imposed, e.g., significance for pairs of F 1 > F 2 > F 3 > F 4 are not necessarily consistent with the order () ( ) ( ) nested LR nested nesting nesting 22 nested nesting nested nesting ˆ ˆˆ 2 log log 2log ˆ 1 L FL L L NF F χχ ⎡⎤ =− ⎣⎦ = θ θθ θ
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• LR test is tedious when we want to find a statistically justifiable “best” fitting model with respect to a set of meaningful constraints; or put differently, when we want to explore for a most optimal model among many alternative substantively justifiable models • Now we need a method that allows for statistical inference about: ¾ What if a set of constraints in a given model is freed?
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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.

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lecture10_s10 CFA - Confirmatory Factor Analysis Model...

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