I wonder if you could help me with/point me toward an example of notation for a linear growth model where the repeated outcome is ordinal. where the outcome is continuous we have:
Yit = alpha(i) + lambda(i)Beta(i) + epsilon(it)
Is there some simple way of modifying this notation to indicate that Y is ordinal? I suppose one could write Y*it where Y* is the latent continuum underlying Y. But would this not also require a specification of the notation for the model linking Y* to Y? thanks in advance, Patrick
You can use the y* approach plus the linking you mention - see Appendix 1 to our UG.
Or, you can express it directly in terms of the observed variables. For example, with a binary u,
log [P(uti = 1 | ii, si , qi, ci, xti) / P(uti = 0 | ii, si , qi, ci, xti)] =
ii + si * (xti – d) + qi * (xti - d)2 + ci * (xti - d)3,
(sorry about the subscripts ti and i) for growth factors i, s, and q. With more than 2 categories you get the logit expression for the ratio of the highest category vs the others, sum of 2 highest vs others, etc as in Appendix 1.
many thanks for this. I have another query regarding the multinomial regression of class membership on covariates in GMM. what do you see as the key statistical benefits of doing this in a single step, rather than running out a group membership variable and regressing this on to the covariates in a separate model? thanks,
If you take the multi-step approach you commit 2 errors. First, the parameter estimates will be biased because you act as if a person is a member of only one class, whereas in the 1-step approach a person occupies all classes fractionally. Second, the SEs will be biased because in the last step you act as if class membership is known, observed (typically you get underestimated SEs).
I am running GMM with ordinal outcome variables (7-point scale) repeatedly measured over 6 time points. I used "categorical" option in Mplus 6.1 and got the probabilities of each category. From the plot option, I got the plots of each category. But I am not very interested in specific patterns of individual categories. Instead, I want to see the overall pattern by taking into account all categories. My question is if it would be okay to treat them as continuous even though they are ordinal variables. I read your article (2002)"General growth mixture modeling for randomized preventive interventions" and I think you treated the 6-point-scale ordinal outcome (TOCA-R) variables as continuous. Is it right?
I know this will depend on research question. Thus, I may be okay to treat the variables as continuous, but I am also uncomfortable to treat them in that way because they are not continuous. What would you recommend for my case? Many thanks in advance.