PROC FMM PROBMODEL Output Interpretation

[jl4443]

Is it correct that the exponentiated estimates from the PROC FMM PROBMODEL statement output correspond to odds ratios for subgroup membership? The output table header says "Parameter Estimates for Mixing Probabilities" and the documentation indicates that they are on the logit scale, and they seem to correspond to log-odds ratios, but that isn't directly stated in any of the documentation or examples I have come across.

If the estimates are indeed log odds ratios, is there anyway to get SAS to exponentiate and output the odds ratio estimates directly? (The fact that it doesn't automatically is what made me question whether this is the proper interpretation, though it does seem to be the case).

I appreciate any thoughts on this - thanks in advance. 

[SAS_Rob]

The short answer is that no, FMM will not report the exponentiated estimates for the mixture probability model(s). 

That being said, it isn't clear what exactly you mean by subgroup membership.  The mixture is a mixture of components and not different models based on some group membership.  I am not sure of what use an odds ratio would be in relation to the various components as I have  never seen anyone report it or clearly define it.  In some cases, you might want to predict the component membership based on some rule(usually the highest posterior probability), but this would not really be related to any kind of odds ratio calculation.

[jl4443]

Thanks for your response. I am trying to quantify the extent to which a covariate in the PROBMODEL statement influences subgroup membership. The probabilities on the logit scale as they are output are not straightforward to interpret, so I was thinking of potentially reporting something like 'covariate level A vs B is associated with increased likelihood of membership in the second subgroup (OR xx, 95% CI xx, xx)'. The benefit of reporting the odds ratio instead of the change in predicted probability would be that the values of the other covariates do not need to be specified. 

[Season]

I guess you are using interchangeably the concept of components- a term in finite mixture models; and subgroup- a word coined by yourself and may be more suitable for your analysis.

PROBMODEL Statement :: SAS/STAT(R) 14.1 User's Guide says that the PROBMODEL statement is used for building regression models (usually logistic regression) for component membership. Odds ratios and other common metrics reported in logistic regression can be calculated from the table named "Parameter Estimates for Mixing Probabilities" in the output.