# Mean versus imputation for missing data in the case of an ordinal scale

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!

• How can ordinal scale (which is categorical, not just discretized) can ever have a specific mean? Jul 4 '14 at 4:17

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

• In light of @ttnphns's comment, it would be nice if you could briefly explain how MI works in the case of categorical variables.
– chl
Feb 3 '15 at 19:52
• @chl, you should quantify the manner in which it is "best." How are you defining "best" here? Feb 4 '15 at 17:11
• @StatsStudent I am not sure to follow: Where did I talk about something "best"?
– chl
Feb 4 '15 at 17:27
• Sorry, chl, I meant to have directed that comment toward @nolanconaway who indicated "the best choice is to use an R package like mi." Feb 4 '15 at 17:32

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.

References

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.

• You cannot just blindly apply multiple imputation to your data. We must have a better understanding of the data before applying this method. There are assumptions that must be made (and preferably verified) before using multiple imputation. for example, the data must be missing at random (MAR). Furthermore, the model used to generate the imputed values must be correct, among others. There are multivariate tests for MAR that can be applied for this. A careful look at the data & understanding of the data is required before applying any type of imputation, lets your risk biasing your estimates. Feb 4 '15 at 17:16
• @StatsStudent My answer was in the context of the OP. Can your provide an example where simple mean or mode replacement in ordinal data performs better than multiple imputation? Feb 5 '15 at 2:21
• Well, @Alexis, since you never defined, "best," I'd argue that mean or mode replacement is the best choice in terms of simplistic imputation strategies. But more to my point, mean and mode replacement aren't the only remaining choices. Other viable solutions include, hot deck imputation procedures, parametric fractional imputation, cold-deck imputation, stochastic regression imputation, etc. Feb 5 '15 at 3:29
• @StatsStudent All of which entail precise the same limitations you are raising in your original comment, and all of which run afoul per Rubin's argument that (absent actual knowledge of the determinants of missingness in NCAR data) all single imputation regimes (a) fail to estimate variability/uncertainty due to missingness, and (b) produce less statistical validity that multiple imputation regimes. Feb 5 '15 at 20:43