Maximum Likelihood vs. Multiple Imputation (combined with Hierarchical Regression)

[Elias Kurta]

I am currently trying to complete my data set with partially missing independent variables. I am considering, if I should use:
- Multiple Imputation, or
- Maximum Likelihood

At the end I would like to perform a hierarchical regression (command: "hireg"). What would be the better / more proper variant?

Many thanks in advance.

[Richard Williams]

Welcome to Statalist.

If you can fit a linear model using sem, then you can use the option

method(mlmv)

to use Full Information Maximum Likelihood. When fiml is possible it has many advantages. It is easy to specify, and (unlike MI) you get the same results every time.

hireg is an incredibly old command though, and pretty much superceded by nestreg. If you want to use fiml, you'll have to use sem.

MI works with many more commands (at least in Stata) so it is more flexible. e.g. As far as I know, fiml is not possible with things like logistic regression (at least not with Stata).

The user-written command xtdpdlm is a shell for sem. To see how it can use MI or FIML, see

https://www3.nd.edu/~rwilliam/dynamic/mi_xtdpdml.pdf

[Richard Williams]

FYI, Allison has a couple of blog entries on FIML vs MI:

https://statisticalhorizons.com/ml-better-than-mi

https://statisticalhorizons.com/ml-is-better-than-mi

In general Allison is a big fan of FIML, but he also notes that MI is sometimes better or at least necessary. Personally, I would like Stata to make the use of FIML broader and easier.

[Elias Kurta]

Many thanks for your response, Richard! To sum up, I have two potential options in STATA:

- Using Maximum Likelihood (FIML) to finalize my variables, but then I have to use SEM instead of hireg/nestreg (whereas nestreg is the more modern one) for analysis
- Using Multiple Imputation (MI) to finalize my variables, and then I can use hireg/nestreg for analysis

I would personally prefer FIML, but not sure if SEM delivers a similar result than hireg/nestreg at the end.

[Richard Williams]

I don't know if MI and nestreg work together or not. I have never tried it.

In any event, nestreg is mostly a convenience. You can write separate commands for each model you want.

I would check the Ns with each reported model. If the Ns are different, it may be that the added variables in a model are losing you cases in spite of what you are doing to handle missing data, e.g. maybe some missing values can't be imputed.