# is a threshold model on ordinal data ~ a link function? SEM OpenMx

Are anyone familiar with OpenMx's capacity for handling ordinal data in SEM using a link function like ordered logit or probit (Stata gsem does this)?

Some folks have highlighted issues with feeding polychoric matrix data to SEM and CFA, so I look for alternatives (otherwise Lavaan enables that easily).

I have read that OpenMx enables threshold models akin to probit. But I have also read that it does not support link functions. I am a little puzzled about how to understand this. This is the documentation:

Maximum likelihood estimation for ordinal variables is done by generating expected covariance and mean matrices for the latent continuous variables underlying the set of ordinal variables, then integrating the multivariate normal distribution defined by those covariances and means. The likelihood for each row of the data is defined as the multivariate integral of the expected distribution over the interval defined by the thresholds bordering that row’s data.

OpenMx uses Alan Genz’s SADMVN routine for multivariate normal integration (see http://www.math.wsu.edu/faculty/genz/software/software.html for more information). When continuous variables are present, OpenMx utilizes a block decomposition to separate the continuous and ordinal covariance matrices for FIML. The likelihood of the continuous variables is calculated normally. The effects of the point estimates of the continuous variables is projected out of the expected covariance matrix of the ordinal data. The likelihood of the ordinal data is defined as the multivariate integral over the distribution defined by the resulting ordinal covariance matrix.

Now also raised here.

• Cross-posted at stackoverflow.com/questions/76472273/… See firm advice in the Help Center that you should please NOT cross-post within SE. stats.stackexchange.com/help/on-topic Commented Jun 14, 2023 at 10:02
• Thanks @NickCox. Do you have suggestions on where to post when the package the question is partly about suggests asking on SO, but the question is also about stats (link functions and threshold models), while SO is AFAIK for code/script and CV is for stats? It does not seem entirely straight. Commented Jun 14, 2023 at 14:47
• Sorry, no suggestions. It sounds from what you say that people responsible for a package are unable or unwilling to answer questions about it. If so, that sounds a poor show. Commented Jun 14, 2023 at 15:26