When performing imputation on categorical variables, does the data lose meaning?

Question

Suppose I have a data set with several variables where one of my variables is categorical. For instance, a rating from 1 to 10. Suppose it has missing values. I want to impute this data via regression or via the mean from another column. However, if I do this, I will get non-integer values in my data.

Will my data lose meaning if there are non-integer values? While I understand summary statistics like the mean can have non-integer values (e.g. 10.5 people), I am unfamiliar with imputation. For instance, if my data was comprised of survey entries, it would seem strange to have values in that column that couldn't have been filled out by the respondents, like 6.34 on a 1 to 10 scale where 6.5 wasn't an option for the respondents.

Are there separate imputation methods that should be used for categorical variables to avoid this problem? If categorical is too general, then please make the answer specific to rating scales like the example I gave.

Answer 1

There are imputation strategies which respect the ordinal nature of your data.

1. You could fill in the missing data with the mode (rather than the mean) of the non-missing data.
2. You can fill in the missing data by sampling from the non-missing data with probabilities proportional to the frequency of occurrence (possibly repeating this many times).
3. A "hot deck imputation" approach, where the data is filled in using data from a similar unit.
4. For a regression approach, you can use ordinal regression (rather than linear) to estimate the missing data

More to the point of your question, a non-integer value like $6.34$ may or may not be inappropriate. This largely depends on how you plan to use the data and what statistical methods you plan to use. In my opinion, it is best to use strategies which maintain the desired structure of the data.