Multivariate Ordinal Mixed Model
Message/Author
 Rachel Dyane Upton posted on Wednesday, October 22, 2008 - 2:25 pm
I am trying to run a joint multilevel logistic regression model with 3 dependent ordinal variables. My goal is to incorporate the correlation between the 3 outcomes, as well as to depict the outcomes as representing 1 latent construct.

Thus, I wanted to know if my Mplus code is correct for what I am trying to do. My data is clustered with a sample size of about 6100, and the data are cross-sectional.

I have one covariate right now- -gender, and I also coded it such that I could estimate random intercepts for each dependent variable.

Here is a copy of what I programmed in Mplus. Can someone please tell me if this is correct, based on what I want to model?

CATEGORICAL = b4c b4a b4d ;
WITHIN =gender;
CLUSTER =site;
MISSING ARE ALL . ;
ANALYSIS:
TYPE = TWOLEVEL;
ESTIMATOR=ML;

MODEL:

%BETWEEN%
b4a b4c b4d;

%WITHIN%
b4a on gender;
b4c on gender;
b4d on gender;
 Bengt O. Muthen posted on Thursday, October 23, 2008 - 9:28 am
This looks fine as far as it goes. But you said you wanted to incorporate a correlation between the 3 DVs (beyond what is caused by the covariate influence) using a factor, which you can do on Within, saying

fw BY b4a b4c b4d;

Also, on Between you want to make sure that there can be a correlation betweeen the 3 random intercepts b4a, b4c, and b4d. So either use WITH statements, or add a factor there as well, fb BY....
 Rachel Dyane Upton posted on Thursday, October 23, 2008 - 1:45 pm
Thanks so much for the response! I actually just ran a model using the WITH statement to represent the correlation between the 3 random intercepts.

I also wanted to ask 2 other questions:
1.) I see your point about adding a factor on the WITHIN portion of the model since my goal is use a single latent variable to account for the intercorrelations among the observed outcomes. Though doesn't Mplus assume for multilevel proportional odds models that your outcome(s) can be theoretically conceptualized as a representation of a latent continuous outcome (e.g., y*) that is distributed with mean 0 and variance (pi^2/3)? So what I'm asking is, can you not assume that an underlying construct is already present without explicitly defining a factor in the WITHIN portion of the model?

2.) Second, is there any literature I can read up on that explains how a cumulative logit model is defined/parameterized using Mplus? I compared the results of a univariate multilevel proportional odds model using Proc Glimmix in SAS and Mplus, and the random intercept, thresholds, etc. everything looked identical, other than the fact that the signs on the regression coefficient for my one explanatory variable (e.g., Gender) are always switched.

Thanks.
 Bengt O. Muthen posted on Thursday, October 23, 2008 - 2:34 pm
1) Yes, you can consider the model as a y* representation. For the WLSMV estimator and under probit, y*'s can be covaries using WITH, but this is not available with ML probit or logit so you have to use one or more factors to correlate the DVs given covariates.

2) The model is the same as in say Agresti's or Long's books. We write about it in the Tech appendix for version 2 on our web site - see the early part. SAS switches the scoring of a binary covariate.
 Rachel Dyane Upton posted on Friday, October 24, 2008 - 10:30 am
Just to specify, are you saying that in the %BETWEEN% section of the multivariate multilevel model, you can define the covariances among the random intercepts ONLY in the case of using the WLSMV estimator with a probit link. Is this correct?

Is there no other way of specifying a multivariate multilevel model for ordinal data while defining covariances between the random intercepts using