Mplus Users Guide v6.. - Muthén & Muthén

Special Modeling IssuesMISSING DATA ANALYSISrestrictive models. If the chi-square difference value is significant, itindicates that constraining the parameters of the nested modelsignificantly worsens the fit of the model. This indicates measurementnon-invariance. If the chi-square difference value is not significant, thisindicates that constraining the parameters of the nested model did notsignificantly worsen the fit of the model. This indicates measurementinvariance of the parameters constrained to be equal in the nested model.For models where chi-square is not available, difference testing can bedone using -2 times the difference of the loglikelihoods. For the MLR,MLM, and WLSM estimators, difference testing must be done using thescaling correction factor printed in the output. A description of how todo this is posted on the website. For WLSMV and MLMV, differencetesting must be done using the DIFFTEST option of the SAVEDATAand ANALYSIS commands.Mplus has several options for the estimation of models with missingdata. Mplus provides maximum likelihood estimation under MCAR(missing completely at random) and MAR (missing at random; Little &Rubin, 2002) for continuous, censored, binary, ordered categorical(ordinal), unordered categorical (nominal), counts, or combinations ofthese variable types. MAR means that missingness can be a function ofobserved covariates and observed outcomes. For censored andcategorical outcomes using weighted least squares estimation,missingness is allowed to be a function of the observed covariates butnot the observed outcomes. When there are no covariates in the model,this is analogous to pairwise present analysis. Non-ignorable missingdata modeling is possible using maximum likelihood estimation wherecategorical outcomes are indicators of missingness and wheremissingness can be predicted by continuous and categorical latentvariables (Muthén, Jo, & Brown, 2003; Muthén et al., 2010). Robuststandard errors and chi-square are available for all outcomes using the*MLR estimator. For non-normal continuous outcomes, this gives the T 2chi-square test statistic of Yuan and Bentler (2000).Mplus provides multiple imputation of missing data using Bayesiananalysis (Rubin, 1987; Schafer, 1997). Both unrestricted H1 andrestricted H0 models can be used for imputation.435