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European Association of Methodology

Department of methodology and evaluation research

Jena University


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Contributions: Abstract

The performance of maximum likelihood (ML) versus means and variance adjusted weighted least square (WLSMV) estimation in confirmatory factor analysis

Philipp Yorck Herzberg André Beauducel
TU Dresden Universität Mannheim
Germany

Maximum likelihood (ML) estimation is most commonly used in confirmatory factor analysis (CFA) and structural equation modelling. ML-estimation assumes that the observed variables follow the multivariate normal distribution and that they are continuous on a scale with equally spaced intervals. However, most of the data in psychological research are ordinal data and they do not follow the multivariate normal distribution. One approach for analyzing ordinal data is the underlying approach, which assumes that the observed ordinal variables stem from a set of underlying latent continuous variables.

Comparisons of the maximum likelihood (ML) and the weighted least square (WLS) estimator for the analysis of ordinal data revealed that WLS-based standard errors showed high amounts of bias, especially with small samples sizes and moderate loadings. However with increased nonnormality, ML-based parameter estimates, standard errors, and factor intercorrelations indicated also high levels of bias. Recently, Muthén introduced the weighted least square means and variance adjusted (WLSMV) estimator as a refinement of the WLS-estimator. The properties of this estimator for analysis of ordinal data have not yet been systematically investigated. This simulation study compares the ML- and the WLSMV-estimates for different sample sizes (250, 500, 750, 1000) when models vary in terms of number of variables (10, 20, 40 with 1, 2 and 3 latent factors respectively), kurtosis, skewness, and number of categories (2, 3, 5).

The results indicate that the WLSMV-estimator compensates more effectively than the ML-estimator for the estimation bias that is due to the categorical aspects of the variables. Moreover, the WLSMV-estimator leads to acceptable standard errors of the model parameter even with sample sizes of about 500 cases, so that the WLSMV-estimator should be regarded as an interesting alternative to the ML-estimator for many research settings.