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I estimated the effect of antisocial behavior (a composite varible of sixdummy variable) on crime by using probit regression. I want to compare it with a model in SEM setting to see if measurement error matters. In SEM, I used following variables.  Crime (binary outcome)  Six factor indicators (all dummies)  One factor (antisocial behavior)  All other covariates predicting crime My MPLUS commands... VARIABLE: CATEGORICAL ARE ccheat ccruel csorry cbreak cdisob ctrbt crime; MODEL: anti by ccheat* ccruel csorry cbreak cdisob ctrbt; anti@1; crime on anti chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi; So, my questions are 1) In order to compare an above SEM model with a usual regression model, should I force correlations among variables (between a latent variable and other exogenous control variables or among control variables) by putting a "with" command? 2) In this setting (categorical outcome, categorical factor indicators, continuous latent variable), which estimator  WLSMV or ML is appropriate? In my understanding, WLSMV is more appropriate for categorical outcomes. But, factor loadings and the coefficient of latent variable on crime are different between two estimators. Thanks, 


How are you going the compare these models  by comparing parameter estimates or loglikelihoods? 

YouGeon Lee posted on Wednesday, August 05, 2009  10:12 am



I just want to compare estimates, especially antisocial behavior. 


Then I would use maximum likelihood and the following two models: MODEL: anti by ccheat* ccruel csorry cbreak cdisob ctrbt; anti@1; crime on anti chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi; MODEL: crime on antisum chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi; Weighted least squares and maximum likelihood are both appropriate for categorical outcomes. In Mplus, weighted least squares estimates probit regressions. Maximum likelihood can estimate either logistic regressions or probit regressions. Weighted least squares is advantageious for models with many factors and residual covariances whereas as maximum likelihood is advantageous for models with few factors and many factor indicators. For ML and categorical indicators, each residual covariance is one dimension of integration. 

YouGeon Lee posted on Wednesday, August 05, 2009  11:46 am



Thanks so much. I got it. What about my first question? I don't need to specify correlations among independent variables by using a command line of "anti with chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi", right? Does it mean that this model without the "with" command assumes no correlations among independent variables? If not, why does it differ from a model with the "with" command? So many thanks... YouGeon 


When you use the factor, you need to have the WITH statement. See below. MODEL: anti by ccheat* ccruel csorry cbreak cdisob ctrbt; anti@1; crime on anti chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi; anti WITH chyper crrecs1 cmaths1 afqt smokedp boy adadhh apovc anumkid hmtot56 nmarryi; You do not need it in the other model where the covariates are correlated. 


Thanks so much!!! 

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