Model fit indices and standardized estimates after multiple imputation and mi estimate, cmdok: sem

[Magdalena Uerlich]

Hi all,

Could someone tell me how I get model fit indices and standardized estimates after having done multiple imputation and used structural equation modelling through the cmdok function?

After the command mi estimates, cmdok: sem I typed the commands sem, standardized and estat gof, stats (all). I get last estimates not found error messages or not valid error messages.

Why is that the case and how can I get around that?

Thanks for your help.

[daniel klein]

Why is that the case and how can I get around that?

There are two aspects to your questions, a technical and a substantial one. I believe the latter should be addressed first.

Multiple imputation was designed to get point estimates and their standard errors correct when there are missing (at random) values. Model fit, even basic measures such as R-squared in linear regression, are arguably not the main focus in the MI framework. One reason is that there is not one model for which you can assess the fit; there are M models. A similar argument could be made for standardized coefficients. These are based on the sample standard deviation of the variables. Unfortunately, there is no longer one sample, there are M samples, hence M standard deviations of a variable (if any values are imputed).

If you think that model fit indices and standardized coefficients make sense in this framework, then you can move on to the technical part of your questions on a workaround. This FAQ explains how to get a point estimate for R-squared. The approach should easily extend to other fit indices. Before you go ahead with this, keep in mind that fit indices, such as CFI, that are typically used in SEM might not qualify as estimates of population parameters and are probably not normally distributed.

Regarding standardized coefficients, you could standardize the variables in each of your imputed datasets before running the models. This can be tricky, technically, because it might lead to so-called super-varying variables; look that latter term up in the glossary of the pdf documentation of [MI]. Whether that approach is theoretically sound, I cannot tell for sure.

In general, sometimes when Stata refuses to do something you ask for, it does so for good reasons. I am not implying that this is always the case and I am not even implying that it is the case here; you will have to judge for yourself. All I am trying to get across is: think about substantial reasons for apparent limitations before jumping to technical workarounds.

Best
Daniel