lecture9_s10 CFA - Confirmatory Factor Analysis Evaluation...

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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 ˆ , − S Σ ˆ ≠ Σ S ˆ − S Σ • Residuals indicate how the specified model predicts individual covariances --- note that the variances s ii have no residual in recursive models • Sources of residuals: ¾ Σ ≠ Σ ( θ ), which we want to know by the residuals ¾ 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 ˆ ij ij s σ − RMR (root mean-square 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 ˆ RMR 2 1 q i ij ij i i j j s q q σ = ≥ = ⎛ ⎞ − ⎜ ⎟ = ⎜ ⎟ + ⎝ ⎠ ∑ ∑ ( ) ( ) ( ) 1/2 1/2 2 N.R. ˆ residual avar residual ˆ ˆ ˆ ij ij ii jj ij s N σ σ σ σ − = = + • RMR represents average residual, as SD indicates an average deviation of a variable around its mean Chi-square test (Browne, 74, 82, 84) 5 • The most common parametric statistical test for overall fit...
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lecture9_s10 CFA - Confirmatory Factor Analysis Evaluation...

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