fitfunction is not finite

Let me make sure I understand. You have 9 ordinal variables, each of which, according to your script, has 7 levels (6 thresholds). Each participant has non-missing data for no fewer than 1 and no more than 3 of the 9 variables. Finally, participants are clustered in twin pairs. Is this right?

If I understand correctly, then yes, I would not be at all surprised if your problems are due to lots of missing data. The model may be empirically unidentified if, for example, there is not a single person who has non-missing data for both variables #5 and #6, since the data would therefore contain no information whatsoever about the polychoric correlation between those two variables. The data might also be too sparse to adequately estimate 7*9 = 63 thresholds per zygosity-sex group. Basically, my suspicion is that this fully saturated model is trying to estimate more parameters than is realistic for the given dataset. How big is the sample and the zygosity-sex groups?

There are a few things you could try:

• You could collapse ordinal categories into one another, so that you have (say) 3 instead of 7. You'd be estimating fewer thresholds that way. But, only do this if the way you combine categories makes sense from a subject-matter perspective.
• You could constrain some parameters to equal one another. For instance, you could assign the same parameter labels to the thresholds in the MZM and DZM groups.
• You could skip fitting a "saturated" model and proceed with the twin model(s) of interest.
• If the nine variables each correspond to a particular age at which a participant could have been assessed, maybe something like biometric latent growth modeling would be preferable? That is, if you have the same phenotype, but measured at different times for different participants, maybe it's not the best choice to treat it as 9 different variables.
• Maybe try to regularize the polychoric correlation matrices with an inverse Wishart prior? I've done this before for covariance matrices, but I'm not sure it's valid to do with correlation matrices.

Edit: That should be 6*9=54 thresholds per zygosity-sex group.

Hi Karoline

I agree with Rob that using a Stand matrix type would be better. I'd typically start correlations at zero not .8 because that is further from being non-positive definite. This is likely the issue with the model going to places where the likelihood is not a positive number. It may prove difficult to avoid this altogether with direct estimation of the correlations as you have it, because it doesn't take much for them to get 'out of sync' with each other (if A and B correlate .99, A and C correlate .8 but B and C correlate -.5 it would not be consistent).

One way to avoid this is to use the Cholesky decomposition (this was the original purpose of the Cholesky). You could consider fixing the first two thresholds for every variable at zero and 1, estimating means, and estimating the covariance matrix as L %*% t(L) where L is a lower triangular matrix. The results you'd get would not be standardized, but they could easily be standardized after the fact (or even in the script) as stnd(L %*% t(L)). Given reasonable starting values, the model should run without trouble.

A disadvantage is that standard errors would be of the cholesky parameters, not the correlations. Two options might be viable to overcome this. One would be to request confidence intervals (but this might take a long time to run). Another might be to use the correlation estimates as starting values for the standardized model you first thought of. This is easier than it seems, since they could be calculated after the first step and plugged in directly in the second. A third would be to get some very clever person like Rob to figure out what the SE's of a correlation matrix should be, given the SE's on its unstandardized Cholesky.

Hi Karoline

I agree with Rob that using a Stand matrix type would be better. I'd typically start correlations at zero not .8 because that is further from being non-positive definite. This is likely the issue with the model going to places where the likelihood is not a positive number. It may prove difficult to avoid this altogether with direct estimation of the correlations as you have it, because it doesn't take much for them to get 'out of sync' with each other (if A and B correlate .99, A and C correlate .8 but B and C correlate -.5 it would not be consistent).

One way to avoid this is to use the Cholesky decomposition (this was the original purpose of the Cholesky). You could consider fixing the first two thresholds for every variable at zero and 1, estimating means, and estimating the covariance matrix as L %*% t(L) where L is a lower triangular matrix. The results you'd get would not be standardized, but they could easily be standardized after the fact (or even in the script) as stnd(L %*% t(L)). Given reasonable starting values, the model should run without trouble.

A disadvantage is that standard errors would be of the cholesky parameters, not the correlations. Two options might be viable to overcome this. One would be to request confidence intervals (but this might take a long time to run). Another might be to use the correlation estimates as starting values for the standardized model you first thought of. This is easier than it seems, since they could be calculated after the first step and plugged in directly in the second. A third would be to get some very clever person like Rob to figure out what the SE's of a correlation matrix should be, given the SE's on its unstandardized Cholesky.