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 gibbon lab posted on Tuesday, December 14, 2010 - 11:30 pm
I have path analysis with one of the paths having a binary dependent variable. I use the command "categorical are " to define the binary outcome. Mplus ask me to use the theta parameterization to run the model. I have no idea how to interpret the parameters under theta parameterization. Can you tell me where to find an example output and interpretation? Or briefly tell me the interpretation. Thanks a lot.
 Linda K. Muthen posted on Wednesday, December 15, 2010 - 2:34 pm
The Theta parameterization is required when a mediator is categorical. This does not change the interpretation of the model. Probit regressions are still estimated.
 gibbon lab posted on Wednesday, December 15, 2010 - 4:55 pm
I see. Will the interpretation of the coefficient of the categorical mediator change? The mediator is coded as 0/1. Usually its coefficient is interpreted as the mean difference of the outcome between the two groups. Will this interpretation change under theta parameterization? Thanks a lot.
 Linda K. Muthen posted on Wednesday, December 15, 2010 - 11:11 pm
For categorical variables, it is the difference in thresholds.
 gibbon lab posted on Thursday, December 16, 2010 - 1:20 pm
Suppose here is my regression with a binary categorical predicitor (B) and a continuous dependent variable (A):
A on B.
The estimated coefficient of B is beta. You mean beta is interpreted as the difference in thresholds? Can you be more specific? Thanks a lot.
 Linda K. Muthen posted on Thursday, December 16, 2010 - 3:12 pm
The scale of the dependent variable determines the type of regression coefficient that is estimated. The scale of the independent variables is irrelevant because the model is estimated conditioned on these variables. In regression, independent variables can be binary or continuous. In both cases they are treated as continuous.

A linear regression coefficient is estimated for a continuous dependent variable. A probit or logistic regression coefficient is estimated for a categorical dependent variable.
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