Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 12• 12.11: Monte Carlo simulation study for a two-level mediationmodel with random slopes• 12:12 Monte Carlo simulation study for a multiple group EFA withcontinuous factor indicators with measurement invariance ofintercepts and factor loadings* Example uses numerical integration in the estimation of the model.This can be computationally demanding depending on the size of theproblem.MONTE CARLO DATA GENERATIONData are generated according to the following steps. First, multivariatenormal data are generated for the independent variables in the model.Second, the independent variables are categorized if requested. Thethird step varies depending on the dependent variable type and the modelused. Data for continuous dependent variables are generated accordingto a distribution that is multivariate normal conditional on theindependent variables. For categorical dependent variables under theprobit model using weighted least squares estimation, data forcontinuous dependent variables are generated according to a distributionthat is multivariate normal conditional on the independent variables.These dependent variables are then categorized using the thresholdsprovided in the MODEL POPULATION command or thePOPULATION option of the MONTECARLO command. Forcategorical dependent variables under the probit model using maximumlikelihood estimation, the dependent variables are generated according tothe probit model using the values of the thresholds and slopes from theMODEL POPULATION command or the POPULATION option of theMONTECARLO command. For categorical dependent variables underthe logistic model using maximum likelihood estimation, the dependentvariables are generated according to the logistic model using the valuesof the thresholds and slopes from the MODEL POPULATION commandor the POPULATION option of the MONTECARLO command. Forcensored dependent variables, the dependent variables are generatedaccording to the censored normal model using the values of theintercepts and slopes from the MODEL POPULATION command or thePOPULATION option of the MONTECARLO command. Forunordered categorical (nominal) dependent variables, the dependentvariables are generated according to the multinomial logistic modelusing the values of the intercepts and slopes from the MODEL360