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The Poor Fit of Model Fit for Selecting Number of Factors in Exploratory Factor Analysis for Scale Evaluation

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Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices: root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker-Lewis index (TLI), and two equivalence test-based model fit indices: RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis. Our results show that all fit indices, except SRMR, are overly sensitive to correlated residuals and nonspecific error, resulting in solutions that are overfactored. SRMR performed well, consistently selecting the correct number of factors; however, previous research suggests it does not perform well with categorical data. In general, we do not recommend using model fit indices to select number of factors in a scale evaluation framework.

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