Why Maximum Likelihood is Better Than Multiple Imputation
Why Maximum Likelihood is Better Than Multiple Imputation
Key takeaways
Bibliography: Allison, P., 2012. Why Maximum Likelihood is Better Than Multiple Imputation. Statistical Horizons. URL https://statisticalhorizons.com/ml-better-than-mi/ (accessed 5.15.23).
Authors:: Paul Allison
Collections:: To Read, Methods
First-page:
I’ve long been an advocate of multiple imputation for handling missing data. For example, in my two-day Missing Data seminar, I spend about two-thirds of the course on multiple imputation, using PROC MI in SAS and the mi command in Stata. The other third covers maximum likelihood (ML). Both methods are pretty good, especially when […]
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Reading notes
The other big problem with multiple imputation is that, to be effective, your imputation model has to be “congenial” with your analysis model. The two models don’t have to be identical, but they can’t have major inconsistencies. And there are lots of ways that they can be inconsistent. For example, if your analysis model has interactions, then your imputation model better have them as well. If your analysis model uses a transformed version of a variable, your imputation model should use the same transformation. That’s not an issue with ML because everything is done under a single model.
One other attraction of ML is that it produces a deterministic result. By contrast, multiple imputation gives you a different result every time you run it because random draws are a crucial part of the process. You can reduce that variability as much as you want by imputing more data sets, but it’s not always easy to know how many data sets are enough.
The catch with ML is that you need specially designed software to implement it. Fortunately, in recent years several major statistical packages have introduced methods for handling missing data by ML. For example, the default in most mixed modeling software (like PROC MIXED in SAS or the xtmixed command in Stata) is to use ML to handle missing data on the response variable. For linear models with missing data on predictors, there are now easy-to-use implementations of ML in both SAS (PROC CALIS) and Stata (the sem command). For logistic regression and Cox regression, the only commercial package that does ML for missing data is Mplus.