Seemingly Unrelated Regression (SUR) for ordered logit and random effects

[Gurdil Gill]

Dear All,

I am using STATA 16.

I am trying to estimate a SUR model.

Brief Data: My four dependent variables are categorical and ordered. For these four equations, I have a different set of independent variables, where a few variables are common between equations. I suspect the errors to be correlated across equations as they may share some unobserved factors. Finally, I want to include crossed random effects.

What I tried:

• The sureg command does not allow ordinal dependent variables.
• I thought of using four different ordered logistic models with mixed effects and then using the suest command that runs saved model estimates. But suest does not allow models with crossed random effects.
• I tried GSEM model. It was good for ordinal dependent variables and allowed crossed random effects. However, I could not include correlated errors.

I would appreciate help in including the correlation among errors in GSEM. Or, please share any information about other alternatives to specify my model.

Thanks for the help!

Kind Regards,
Gurdil

[Richard Williams]

gsem does not allow correlated errors in this case.

Perhaps you could create a latent variable that directly affected your independent variables. It would reflect the influence of the unobserved variables that you think should cause correlated errors.

That is just a guess though; I haven't actually tried it.

[Gurdil Gill]

Dear Richard,

Thanks for your response.

I understand the logic behind introducing a latent variable. I tried this approach but the model stopped with "discontinuous region encountered."

Also, I wish to generate a correlation matrix of residuals from different equations, just the way sureg command allows. I believe the above-mentioned approach with GSEM may not allow that.


On another note, I am thinking of converting my ordinal dependent variables to continuous. I hope to find a command similar to sureg that allows me to add random effects and generates a correlation matrix.

In this approach, I am not yet confident in converting my ordinal outcomes to continuous. Currently, they are based on Likert scale ("strongly agree", "somewhat agree", "somewhat disagree", "strongly disagree"). Could I assign -2, -1, 1, and 2 (in that order) to make them continuous? The literature provides mixed opinions on such conversions.

Best,

Gurdil

[Joseph Coveney]

Richard seems to understand it, but I have to confess to being confused by your request. I would have approached the matter by setting up a statistical model to fit what I think the data-generating process is doing. What do you see as the data-generating process, especially in terms of this residual variance in whose correlations you’re interested? What do the “equations” that you mention look like—the equations’ terms, especially for the latent variables (including error variances and their covariance) that underlie the manifest ordered-categorical variables? What are the equations’ identifying restrictions and how is the covariance of interest accommodated in their presence?

I’m guessing that once you’ve gone through that exercise, if you haven’t already, then the syntax of the ordered-categorical SEM with its cross-classified random effects and “correlated errors” will become clear.

Regarding treating ordered-categorical outcome variables as continuous, I agree that the literature is divided on the prospect, and you can find cogent arguments on both sides. My advice is to try simulating ordered-categorical data from known parameters of interest in artificial datasets that have the essential characteristics as yours (sample size, number of categories and their marginal distribution's skew, kurtosis and so on) and seeing whether the statistical model that you plan to use reliably gives results that are at least acceptably consistent with them for practical purposes.