A Comparison of Diagonal Weighted Least Squares Robust Estimation Techniques for Ordinal Data

This study compared diagonal weighted least squares robust estimation techniques available in 2 popular statistical programs: diagonal weighted least squares (DWLS; LISREL version 8.80) and weighted least squares–mean (WLSM) and weighted least squares—mean and variance adjusted (WLSMV; Mplus version 6.11). A 20-item confirmatory factor analysis was estimated using item-level ordered categorical data. Three different nonnormality conditions were applied to 2- to 7-category data with sample sizes of 200, 400, and 800. Convergence problems were seen with nonnormal data when DWLS was used with few categories. Both DWLS and WLSMV produced accurate parameter estimates; however, bias in standard errors of parameter estimates was extreme for select conditions when nonnormal data were present. The robust estimators generally reported acceptable model–data fit, unless few categories were used with nonnormal data at smaller sample sizes; WLSMV yielded better fit than WLSM for most indices.

[1]  Deborah L Bandalos,et al.  Efficacy of the WLSMV Estimator for Coarsely Categorized and Nonnormally Distributed Data , 2005 .

[2]  V. Savalei,et al.  When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. , 2012, Psychological methods.

[3]  S. Finney.  Nonnormal and categorical data in structural equation modeling , 2013 .

[4]  Susan R. Hutchinson,et al.  Behavior of descriptive fit indexes in confirmatory factor analysis using ordered categorical data , 1998 .

[5]  Tron Foss,et al.  Testing structural equation models: The effect of kurtosis , 2011, Comput. Stat. Data Anal..

[6]  K. Jöreskog,et al.  Confirmatory Factor Analysis of Ordinal Variables With Misspecified Models , 2010 .

[7]  B. Muthén,et al.  Computing the Strictly Positive Satorra-Bentler Chi-Square Test in Mplus , 2013 .

[8]  D. Bandalos.  Is Parceling Really Necessary? A Comparison of Results From Item Parceling and Categorical Variable Methodology , 2008 .

[9]  B. Muthén,et al.  A comparison of some methodologies for the factor analysis of non‐normal Likert variables , 1985 .

[10]  Tron Foss,et al.  The Performance of ML, GLS, and WLS Estimation in Structural Equation Modeling Under Conditions of Misspecification and Nonnormality , 2000 .

[11]  James B. Schreiber,et al.  Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review , 2006 .

[12]  Kristopher J Preacher,et al.  Item factor analysis: current approaches and future directions. , 2007, Psychological methods.

[13]  B. Muthén,et al.  Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes , 1997 .

[14]  Margaret J. Potthast,et al.  Confirmatory factor analysis of ordered categorical variables with large models , 1993 .

[15]  A. Boomsma,et al.  Robustness Studies in Covariance Structure Modeling , 1998 .

[16]  R. Purc-Stephenson,et al.  Reporting practices in confirmatory factor analysis: an overview and some recommendations. , 2009, Psychological methods.

[17]  On Chi-Squares for the Independence Model and Fit Measures in LISREL , 2004 .

[18]  D. Flora,et al.  An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. , 2004, Psychological methods.

[19]  André Beauducel,et al.  On the Performance of Maximum Likelihood Versus Means and Variance Adjusted Weighted Least Squares Estimation in CFA , 2006 .

[20]  D. Kaplan.  Structural Equation Modeling: Foundations and Extensions , 2000 .

[21]  Christine DiStefano,et al.  Using Confirmatory Factor Analysis for Construct Validation: An Empirical Review , 2005 .

[22]  Christine DiStefano,et al.  The Impact of Categorization With Confirmatory Factor Analysis , 2002 .

[23]  Alberto Maydeu-Olivares,et al.  Factor Analysis with Ordinal Indicators: A Monte Carlo Study Comparing DWLS and ULS Estimation , 2009 .

[24]  Pui-Wa Lei,et al.  Evaluating estimation methods for ordinal data in structural equation modeling , 2009 .

[25]  猪原 正守.  Comparison of estimation methods in factor analysis , 1986 .

[26]  Stephen G. West,et al.  Structural equation models with non-normal variables: Problems and remedies , 1995 .

[27]  Andreas Ritter,et al.  Structural Equations With Latent Variables , 2016 .