Is mean or mode better for replacing missing data for an ordinal scale? I'm thinking mode is better because the respondent has to choose between integer values (1, 2 and so on) bu I am wondering is mode imputation doesn't create bias by favoring the value that appears most often. Thank you!
The best choice is to use an R package like mi (mice, or amelia should also work). It will scan your data and propose the appropriate format for each variable (which you can also manually change if needed)
In the case of categorical (ordered or not) variables in the MI package - a series of chained, ordinal regressions are run with the variables targeted for imputation as the DVs. This is done until some convergence criteria are met (which can be adjusted in the package
You could think of it as a markov chain of regressions using all included data to predict missing data in all of the variables you included in the analysis
The best choice is multiple imputation (MI), which is an iterative process of probabilistically estimating missing values based on observed information from across your data set. The great thing about MI is that not only does one get (A) decent estimates of the missing data values, one also gets (B) estimates of the increased uncertainty in one's analysis due to data missingness.
Donders, A. R. T., Heijden, G. J. M. G. van der, Stijnen, T., & Moons, K. G. M. (2006). Review: A gentle introduction to imputation of missing values. Journal of Clinical Epidemiology, 59(10), 1087–1091.
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3):581–592.
Rubin, D. B. (1996). Multiple imputation after 18+ years. Journal of the American Statistical Association, 91(434):473–489.
Schafer, J. L. (1999). Multiple imputation: a primer. Statistical Methods in Medical Research, 8:3–15.