Small-Sample Robust Estimators of Noncentrality-Based and Incremental Model Fit

• Published in: Structural equation modeling Vol. 16; no. 1; pp. 1 - 27
• Main Authors: Herzog, Walter, Boomsma, Anne
• Format: Journal Article
• Language: English
• Published: Hove Taylor & Francis Group 01.01.2009; Psychology Press
• Subjects: Computation; Computer Software; Estimating techniques; Goodness of Fit; Intervals; Maximum likelihood method; Monte Carlo Methods; Monte Carlo simulation; Sample Size; Statistical Analysis; Structural Equation Models
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705510802561279

Traditional estimators of fit measures based on the noncentral chi-square distribution (root mean square error of approximation [RMSEA], Steiger's γ, etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartlett's (1950) , Yuan's (2005) , or Swain's (1975) correction of the maximum likelihood chi-square statistic for the estimation of noncentrality-based fit measures. In a Monte Carlo study, it is shown that Swain's correction especially produces reliable estimates and confidence intervals for different degrees of model misspecification (RMSEA range: 0.000-0.096) and sample sizes (50, 75, 100, 150, 200). In the second part of the article, the study is extended to incremental fit indexes (Tucker-Lewis Index, Comparative Fit Index, etc.). For their small-sample robust estimation, use of Swain's correction is recommended only for the target model, not for the independence model. The Swain-corrected estimators only require a ratio of sample size to estimated parameters of about 2:1 (sometimes even less) and are thus strongly recommended for applied research. R software is provided for convenient use.