MI support for user-written commands

[Richard Williams]

I notice that hetprob does not have built-in support for -mi estimate-. Is this because (a) it would be a profound statistical mistake to allow mi with hetprob, or (b) nobody bothered to add support for mi in hetprob?

More generally, with a user-written command, are there guidelines for when the command should or should not provide support for mi?

I occasionally get asked if multiple imputation is ok with my own commands, oglm and gologit2. I am guessing it is ok, but I don't have a good feel for when multiple imputation would be inappropriate with a particular estimation procedure.

[skolenik]

Richard, this is a pretty interesting question, and depends in part on how one interprets these models. Models with underlying choice utility (an econometric interpretation of the logistic models including the ordinal one) assume there's an unobserved error in utility model that has a logistic distribution with fixed variance of sigma = _pi^2/3 which sets the scale of the whole model. Asymptotically, you hope that this will work out for the population model with its utilities (although I don't know if it is explored particularly well in terms of finite samples). Sometimes, you see econometricians argue that only the ratio of beta/sigma is what makes sense in this (utility) model. When you are estimating the ologit model, one would argue that you make an assumption that the sample variance = population variance to identify the model; and hence your ratio of beta/sigma will be overstated if in your particular sample you happened to have a smallish sample variance. Likewise, when you do your multiple imputations, then each imputed set assumes something that is true about the imputed sample (sigma equals _pi^2/3) which we had to use as crutches to even get identification of this model. With these kinds of interpretational issues, does the MI framework provide inference only conditional on the sample, or can it work towards the population figures, as well? I don't really know.

Now, biostatisticians don't even understand this gibberish. For them, the logistic models are simply a calculus of probabilities and odds ratios. Whatever makes sense in terms of odds ratios is good; whatever is just an assumption that can be violated (e.g., proportionality assumptions) can be relaxed to see if this assumption is satisfied (and that's how one can interpret gologit2). (Vice versa, this is gibberish for econometricians; do the more general assumptions of gologit2 mean the slopes of the latent regression are functions of the left hand side variable? That's just weird and illogical.)

So my guess is that if you try this by simulation, you can find two different answers depending on how you simulate your data, including your missing data, even though you won't be able to tell from the complete data (simulated in full accordance with the restrictive ologit model) whether it came from the "econometric" utility model formulation or the "biostat" odds ratio model formulation.

That's just my gut feeling concerning mi. If you are not worried with these interpretational issues, then I would venture a guess that oglm and gologit2 will work just fine with mi, at least in terms of mechanics of forcing it through with mi estimate, cmdok.

[Yulia Marchenko (StataCorp)]

As Stat points out, the cmdok option can be used with mi estimate to allow any estimation command to work with the mi estimate: prefix. The estimation command must still follow specific rules to be able to work properly with mi estimate; see help program_properties##mi for these rules as well as for the information about how to make user-written commands support the mi estimate: prefix.

I also discuss some of the technical requirements for the commands to be officially supported by mi estimate in the following post:

http://www.stata.com/statalist/archi.../msg00479.html

As for the statistical issue of when MI is applicable, in general, procedures which lead to estimators with asymptotically normal sampling distributions and with a consistent estimate of sampling variance/covariance are applicable within the MI framework. More details can be found in, for example, Rubin (1996), which discusses the essential statistical points for the validity of multiple imputation as a statistical procedure.

Reference:
Rubin, D. B. 1996. Multiple imputation after 18+ years. Journal of the American Statistical Association 91: 473-489.

[Richard Williams]

Stas - thanks. Basically I am interpreting your answer as meaning that it is probably no more illegitimate to use oglm and gologit2 with multiple imputation than it is to use them without multiple imputation.

Also thanks to Yulia, I believe my commands meet the technical requirements.

Still unanswered is my very first question: why isn't hetprob hard-coded to support multiple imputation? Because nobody bothered to code it or because it would be statistically wrong to do so? oglm is basically a generalized version of hetprob, so if mi is for some reason wrong for hetprob it may well be wrong for oglm.

[Yulia Marchenko (StataCorp)]

I do not see a statistical or technical reason for hetprobit not to support multiple imputation. We will consider adding this command to the list of commands officially supported by mi estimate in the future.

[Richard Williams]

Reviving this old thread, I notice that hetprob is still not on the list of commands blessed to work with -mi estimate-. Is this because (a) nobody got around to doing it, or (b) serious problems were discovered? If the latter, it seems odd to me that fracreg (which has a het option) works with mi estimate but hetprob does not.

I know you can always just add the cmdok option to mi estimate, but if doing so would be a horrible mistake that would be nice to know.