Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 5above, all six factor indicators are binary or ordered categoricalvariables. The program determines the number of categories for eachfactor indicator. The default estimator for this type of analysis is arobust weighted least squares estimator (Muthén, 1984; Muthén, du Toit,& Spisic, 1997). With this estimator, probit regressions for the factorindicators regressed on the factors are estimated. The ESTIMATORoption of the ANALYSIS command can be used to select a differentestimator. An explanation of the other commands can be found inExample 5.1.With maximum likelihood estimation, logistic regressions for the factorindicators regressed on the factors are estimated using a numericalintegration algorithm. This is shown in Example 5.5. Note thatnumerical integration becomes increasingly more computationallydemanding as the number of factors and the sample size increase.EXAMPLE 5.3: CFA WITH CONTINUOUS ANDCATEGORICAL FACTOR INDICATORSTITLE: this is an example of a CFA withcontinuous and categorical factorindicatorsDATA: FILE IS ex5.3.dat;VARIABLE: NAMES ARE u1-u3 y4-y6;CATEGORICAL ARE u1 u2 u3;MODEL: f1 BY u1-u3;f2 BY y4-y6;The difference between this example and Example 5.1 is that the factorindicators are a combination of binary or ordered categorical (ordinal)and continuous variables instead of all continuous variables. TheCATEGORICAL option is used to specify which dependent variablesare treated as binary or ordered categorical (ordinal) variables in themodel and its estimation. In the example above, the factor indicators u1,u2, and u3 are binary or ordered categorical variables whereas the factorindicators y4, y5, and y6 are continuous variables. The programdetermines the number of categories for each factor indicator. Thedefault estimator for this type of analysis is a robust weighted leastsquares estimator. With this estimator, probit regressions are estimatedfor the categorical factor indicators, and linear regressions are estimatedfor the continuous factor indicators. The ESTIMATOR option of the58