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.