John Lee posted on Monday, June 22, 2009 - 12:50 am
At the Mplus Users Guide V5 (p. 407), it was stated that the P(u=1|x)=1/(1+exp(-a-b*x)).
I have just fitted a simple model on a binary variable (0: 100 times vs 1: 200 times): TITLE: binary variable DATA: FILE IS binary1.dat; VARIABLE: NAMES x w; ! w: frequency FREQWEIGHT IS w; CATEGORICAL ARE x; USEVARIABLES ARE x; MODEL: [x$1]; OUTPUT:
The followings are part of the output: SUMMARY OF ANALYSIS
SUMMARY OF CATEGORICAL DATA PROPORTIONS X Category 1 0.333 Category 2 0.667
MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value
Thresholds X$1 -0.431 0.075 -5.754 0.000
The estimated probability is clearly .667 (200/300). When I do the calculations based on the estimated threshold, it is P(u=1|x)=1/(1+exp(0.431))=.39. Even if I use 1-.39=.606, it is still different from the expected value .667.
For maximum likelihood, the default link is logit. However, the default estimator for categorical outcomes is weighted least squares and probit regression. What you posted does not show which estimator you used. Please send your full output and license number to firstname.lastname@example.org.