# Can you impute (predict) missing continuous data using categorical data as the predictor?

I just read that to use MICE Imputation, variables with missing values need to have a relationship to other variables. In my case, I will anonymize the variable just for convenience purposes:

• Numerical Continuous Variables: 'A', 'B', 'C', 'D'
• Categorical Variables (Nominal): 'X', 'Y'

'A' has missing values of around 20%, while the other variables are complete. Now I read that it's better to impute the values instead of dropping them using techniques such as MICE, Random Forests, kNN, Bootstrapping, etc.

I checked into MICE first, considering it's flexible for all kinds of variables and gives less biased imputations if the model is appropriate. One of the requirements to use MICE is that the variable that will be imputed needs to have a relationship with other variables.

Hence, I analyzed 'A' with other numerical variables and only found a weak relationship between them (around 0.2)

But when I tried to analyze 'A' with other categorical variables using ANOVA, it showed a strong relationship with 'X' and 'Y', plus it's statistically significant (***).

Can I use 'X' and 'Y' (categorical variables) as the predictor in imputing the missing values in 'A' through MICE Imputation?

• You can use them all together - categorical and continuous
– mkt
Mar 17, 2023 at 14:46
• Good point. Can you safely gather insights from the imputed dataset? In this case, I need to do a basic exploratory analysis. Mar 18, 2023 at 8:08

There's no reason not to mix different types of data for multiple imputation (continuous, categorical, ordinal etc.). It's just a matter of whether the particular software you use can support it (e.g. the Amelia R package supports quite a few types of data, but e.g. is still not great for censored data or count data). You may also want to check whether MI via chained equations (MICE) is the most appropriate approach for your situation (for some reason it's very popular, but tends to perform poorly in quite a few simulations I've seen) or other forms like MCMC based with latent multivariate normal assumption (like the default approach in Amelia).

• I see, but is it true that to use MICE, the variables that will be imputed need to have a normal distribution? And if it isn't, then we can't use MICE because it will produce bias, right? Mar 18, 2023 at 8:06
• It's more a potential limitation of some particular implementations. MICE = MI via chained (regression) equations. A regression equation can have non-normally distributed variables as predictors, and there's versions of MICE for various types of data as the "to-be-imputed" data, too. Mar 18, 2023 at 19:01