Mplus Users Guide v6.. - Muthén & Muthén

Examples: Monte Carlo Simulation StudiesCHAPTER 12EXAMPLES: MONTE CARLOSIMULATION STUDIESMonte Carlo simulation studies are often used for methodologicalinvestigations of the performance of statistical estimators under variousconditions. They can also be used to decide on the sample size neededfor a study and to determine power (Muthén & Muthén, 2002). MonteCarlo studies are sometimes referred to as simulation studies.Mplus has extensive Monte Carlo simulation facilities for both datageneration and data analysis. Several types of data can be generated:simple random samples, clustered (multilevel) data, missing data, anddata from populations that are observed (multiple groups) or unobserved(latent classes). Data generation models can include random effects,interactions between continuous latent variables, interactions betweencontinuous latent variables and observed variables, and betweencategorical latent variables. Dependent variables can be continuous,censored, binary, ordered categorical (ordinal), unordered categorical(nominal), counts, or combinations of these variable types. In addition,two-part (semicontinuous) variables and time-to-event variables can begenerated. Independent variables can be binary or continuous. All orsome of the Monte Carlo generated data sets can be saved.The analysis model can be different from the data generation model. Forexample, variables can be generated as categorical and analyzed ascontinuous or data can be generated as a three-class model and analyzedas a two-class model. In some situations, a special external Monte Carlofeature is needed to generate data by one model and analyze it by adifferent model. For example, variables can be generated using aclustered design and analyzed ignoring the clustering. Data generatedoutside of Mplus can also be analyzed using this special Monte Carlofeature.Other special features that can be used with Monte Carlo simulationstudies include saving parameter estimates from the analysis of real datato be used as population parameter and/or coverage values for datageneration in a Monte Carlo simulation study. In addition, analysisresults from each replication of a Monte Carlo simulation study can be357