Mplus Users Guide v6.. - Muthén & Muthén

Special Modeling Issues(2) P (u = r | x) = exp (a r + b r *x) / (exp (a 1 + b 1 *x) + …+ exp (a R + b R *x)),where exp (a R + b R *x) = exp (0 + 0*x) = 1 and the log odds forcomparing category r to category R is(3) log [P (u = r | x)/P (u = R | x)] = a r + b r *x.With an ordered categorical (ordinal) variable, the logistic regressionslopes b r are the same across the categories of u.Following is an example of an unordered categorical (nominal)dependent variable that is the categorical latent variable in the model.The categorical latent variable has four classes and there are threecovariates. The output excerpt shows the results from the multinomiallogistic regression of the categorical latent variable c on the covariatesage94, male, and black:Estimates S.E. Est./S.E.C#1 ONAGE94 -.285 .028 -10.045MALE 2.578 .151 17.086BLACK .158 .139 1.141C#2 ONAGE94 .069 .022 3.182MALE .187 .110 1.702BLACK -.606 .139 -4.357C#3 ONAGE94 -.317 .028 -11.311MALE 1.459 .101 14.431BLACK .999 .117 8.513InterceptsC#1 -1.822 .174 -10.485C#2 -.748 .103 -7.258C#3 -.324 .125 -2.600Using (3), the log odds expression for a particular class compared to thelast class is,log odds = a + b 1 *age94 + b 2 *male + b 3 *black.In the first example, the values of the three covariates are all zero so thatonly the intercepts contribute to the log odds. Probabilities arecomputed using (2). In the first step, the estimated intercept log odds443