Hi, Thank you for so kindly responding to all my questions. As I am preparing to submit an article to a journal employing a parallel process LGM with categorical and continuous data for the first time, I want to be absolutely sure I interpret my data correctly. Regarding my measurement model, is it correct that the appropriate interpretation for my ordered polytomous (smoking status from non-smoker to frequent smoker) variable with a significant positive slope is that the odds ratio (logit, formulas 29 & 30 in appendix 1) is significant, such that over the four time points the probability of advancing to a higher status is greater than chance?
bmuthen posted on Thursday, October 24, 2002 - 12:15 am
Formulas 29 and 30 talk about log odds. I would say that the log odds of being in a higher category is significantly increased over time. Assuming that you have a linear model, the increase (the mean of the slope) is constant from time point to time point and refers to a one-timepoint change. Note also that the estimated log odds coefficient beta can be exponentiated into an odds, and the corresponding confidence limits computed from those of the log odds limits, exponentiated.
I am curious under what conditions Mplus results derived from path analysis and structural equation models can be used to generate odds ratios for interpretation and result presentation purposes when one is modeling binary or ordered categorical outcomes?
(I am excluding TYPE = LOGISTIC from this discussion as my interest is in modeling binary or ordered categorical outcomes as functions within the context of path analysis models or SEMs).
You can generate odds ratios from the probit regression coefficients estimated using weighted least squares or from the logistic regression coefficients estimated using maximum likelihood. In the latter case, you do the usual exponentiation of the coefficients as in logistic regression. In the former case, you have to first compute the probabilities of the odds. See Technical Appendix 1.