# Choosing MICE multiple datasets

I have read and watched several tutorials about MICE. My confusion is about step 1: creating several copies of the original dataset and imputing different values in each copy. In some tutorials, I have seen random subsamples of the original datasets instead of multiple copies of the whole dataset. I am not sure if these two are talking about the same thing or not. If the first statement is the correct one, does it mean that we impute one VARIABLE in each of these copies? If the second statement is correct, how do we choose these random subsamples?

## 1 Answer

The best freely available resource on this topic is probably Stef van Buuren's Flexible Imputation of Missing Data (FIMD). "MICE" stands for "multiple imputation via chained equations," one particular way to do imputation. It might help to keep that distinction in mind.

Each copy of a multiply imputed data set includes imputations of all missing data points, imputations incorporating randomness to acknowledge the variability in imputation. Each is thus a full data set without missing values. Differences in model results among the imputed data sets are used to estimate the error introduced by imputation.

It's not clear from the question just what you mean by "random subsamples of the original datasets." There is random sampling involved in the MICE algorithm (Section 4.5 of FIMD). That, however, is sampling from the conditional distributions of variables among each other within the data set, not subsampling of cases from data sets. Some analysis methods use random subsamples of cases from data sets for cross validation or bootstrapping, but subsampling isn't an imputation method.

So there really isn't an issue in which imputed data sets to "choose." It is critical to make good choices about how to do the imputations and how many imputed data sets to generate.

• Thank you for the reference. I will look into that. About "incorporating randomness to acknowledge the variability in imputation", if we have multiple COPIES of the original datasets, then what is RANDOM? I thought we are randomly selecting some data in each iteration to have a less biased estimate. Mar 9, 2022 at 22:15
• @Hanna I think there's some confusion in the word "copies." Think about starting with multiple copies of the original data set, including all the missing-data cells. Then you fill in all of those missing-data cells separately, with appropriate randomness, for each of those multiple copies. Thus the data sets end up not being exact copies of each other. You generate multiple data copies without missing values, based on the original data. Some imputation methods fill in missing data by sampling from corresponding non-missing data; that might be a source of some confusion.
– EdM
Mar 9, 2022 at 22:44
• Thank you. Yes, I have seen using mean to impute in the first step. You mentioned that we will fill missing cells "with appropriate randomness". We will impute all the missing values at the end of this step so we are not choosing missing values to impute by random. We also will use a method such as mean to impute missing values. So what is random here? Mar 9, 2022 at 23:14
• @Hanna mean imputation doesn’t provide randomness. Multiple imputation samples from distributions of predictions. For example, instead of just choosing the mean you could sample multiple times from a normal distribution around the mean, using the standard error of the mean to set the variance for the sampling.
– EdM
Mar 10, 2022 at 1:21
• @Hanna in the reference you cite, that "simple imputation" is just an initialization step for the MICE procedure. It provides a tentative starting place for the modeled imputation to produce a fully imputed data set with randomness. Those initial "simple imputations" don't show up in the final imputed data set. Then the process repeats for the desired number of (multiple) imputed data sets.
– EdM
Mar 10, 2022 at 21:43