Examining Chi-Square Test Statistics Under Conditions of Large Model Size and Ordinal Data. Issue 6 (2nd November 2018)

• Record Type: Journal Article
• Authors: Shi, Dexin; DiStefano, Christine; McDaniel, Heather L.; Jiang, Zhehan
• Is Part Of: Structural equation modeling. Volume 25:Issue 6(2018)
• Page Start: 924
• Page End: 945
• Publication Date: 2018-11-02
• Subjects: chi-square test statistics -- large models -- ordinal factor analysis; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2018.1449653
• Languages: English
• ISSNs: 1070-5511

Abstract

Abstract : This study examined the effect of model size on the chi-square test statistics obtained from ordinal factor analysis models. The performance of six robust chi-square test statistics were compared across various conditions, including number of observed variables ( p ), number of factors, sample size, model (mis)specification, number of categories, and threshold distribution. Results showed that the unweighted least squares (ULS) robust chi-square statistics generally outperform the diagonally weighted least squares (DWLS) robust chi-square statistics. The ULSM estimator performed the best overall. However, when fitting ordinal factor analysis models with a large number of observed variables and small sample size, the ULSM-based chi-square tests may yield empirical variances that are noticeably larger than the theoretical values and inflated Type I error rates. On the other hand, when the number of observed variables is very large, the mean- and variance-corrected chi-square test statistics (e.g., based on ULSMV and WLSMV) could produce empirical variances conspicuously smaller than the theoretical values and Type I error rates lower than the nominal level, and demonstrate lower power rates to reject misspecified models. Recommendations for applied researchers and future empirical studies involving large models are provided.