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The performance of robust test statistics with categorical data
Author(s) -
Savalei Victoria,
Rhemtulla Mijke
Publication year - 2013
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.2012.02049.x
Subject(s) - statistics , categorical variable , mathematics , statistic , estimator , standard error , test statistic , robust statistics , type i and type ii errors , sample size determination , statistical hypothesis testing , variance (accounting) , accounting , business
This paper reports on a simulation study that evaluated the performance of five structural equation model test statistics appropriate for categorical data. Both Type I error rate and power were investigated. Different model sizes, sample sizes, numbers of categories, and threshold distributions were considered. Statistics associated with both the diagonally weighted least squares (cat‐DWLS) estimator and with the unweighted least squares (cat‐ULS) estimator were studied. Recent research suggests that cat‐ULS parameter estimates and robust standard errors slightly outperform cat‐DWLS estimates and robust standard errors (Forero, Maydeu‐Olivares, & Gallardo‐Pujol, 2009). The findings of the present research suggest that the mean‐ and variance‐adjusted test statistic associated with the cat‐ULS estimator performs best overall. A new version of this statistic now exists that does not require a degrees‐of‐freedom adjustment (Asparouhov & Muthén, 2010), and this statistic is recommended. Overall, the cat‐ULS estimator is recommended over cat‐DWLS, particularly in small to medium sample sizes.