Mplus Users Guide v6.. - Muthén & Muthén

Special Modeling IssuesScale ofDependentScale of Observed MediatingVariableVariable Continuous Censored,Categorical,and CountScale of LatentVariableContinuousContinuous ON ON** ONBYCensored,Categorical,and CountON** ON** ON*BY*Nominal ON** ON** ON*ContinuousLatentON ON** ONBYCategoricalLatentON** ON** ON*BY*Inflation Part ofCensored andCountON** ON** ON*BY*When the posterior distribution does not have a closed form, it isnecessary to integrate over the density of the latent variable multipliedby the conditional distribution of the outcomes given the latent variable.Numerical integration approximates this integration by using a weightedsum over a set of integration points (quadrature nodes) representingvalues of the latent variable.Three types of numerical integration are available in Mplus with orwithout adaptive numerical integration. They are rectangular (trapezoid)numerical integration with a default of 15 integration points perdimension, Gauss-Hermite integration with a default of 15 integrationpoints per dimension, and Monte Carlo integration with integrationpoints generated randomly with a default of 500 integration points intotal. In many cases, all three integration types are available. Whenmediating variables have missing data, only the Monte Carlo integrationalgorithm is available.For some analyses it is necessary to increase the number of integrationpoints to obtain sufficient numerical precision. In these cases, 20-50integration points per dimension are recommended for rectangular andGauss-Hermite integration and 1000 total integration points for MonteCarlo integration. Going beyond these recommendations is notadvisable because the precision is unlikely to be improved any further,419