Does OpenMx estimate the ordered family using a link function like probit or logit? Or may I open a feature request on github?
I found one years old Q&A [6] in this forum here stating the the threshold model was akin to the probit. And this other Q&A [7] mentions how to specify a probit model. So I am asking this question for a clearer answer.
It puzzles me that I cannot find software (besides perhaps Stata) that enables estimating a SEM with latent factors using family link functions (e.g. ordered + logit). As far as I understand, only with that method, the factors are estimated in relation to the distribution of the items. Please let me know if you believe there are reasons that this is mistaken or not important.
"Categorical Threshold Estimation -- Models with categorical outcomes can be estimated, including thresholds for the categories."
- openmx-features [8]
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.
- documentation [9]