As a step to building a larger SEM, I am currently trying to fit a MIMIC CFA with ordinal indicators.

As demonstrated in the sample script and dataset, the model (using ML) with continuous variables the model is identified and no error is thrown.
If I recode variables as ordinal, and add thresholds to the model I get the error messages differing based on fit function.

1. Continuous models provides estimate sizes within a range that what would seem reasonable, the model is locally identified, and no error messages are returned.

2. An equivalent ordinal model, with with added thresholds, fit with ML, returns the error: "Information matrix is not positive definite (not at a candidate optimum).
Be suspicious of these results. At minimum, do not trust the standard errors." Fit function is locally identified (mxCheckIdentification()), but the estimates are unresonable.

3. An equivalent model fit with WLS, returns the same error as fitting the ordinal model with WLS. Only now I also the following error from mxCheckIdentification() and mxStandardizeRAMPaths: "Error in solve.default(I - A) :
system is computationally singular: reciprocal condition number = 1.92319e-31"

I am trying to understand what these error messages mean, and why they occur with ordinal variables and not with continuous data? Is there a way avoid this from happening? For example, does the data lack sufficient power to handle adding thresholds?

Supplementary information:

The larger SEM I'm trying to model, this factor is the main predictor. Since it has multiple factors with ordinal indicators, WLS is realistically the only way I can fit the larger model. The SEM model keep throwing error messages, and estimates that are both disproportionate and inconsistent when I try fit the data with this factor and its ordinal indicators. The problem seem to be with this particular factor (see attached script and dataset), as the same errors are thrown when I run it as a CFA. Also, the SEM will not throw an error if this factor and indicators are either removed or its indicators are added as continuous.