A Comparison of Imputation Strategies for Ordinal Missing Data on Likert Scale Variables

Abstract

This article compares a variety of imputation strategies for ordinal missing data on Likert scale variables (number of categories = 2, 3, 5, or 7) in recovering reliability coefficients, mean scale scores, and regression coefficients of predicting one scale score from another. The examined strategies include imputing using normal data models with naïve rounding/without rounding, using latent variable models, and using categorical data models such as discriminant analysis and binary logistic regression (for dichotomous data only), multinomial and proportional odds logistic regression (for polytomous data only). The result suggests that both the normal model approach without rounding and the latent variable model approach perform well for either dichotomous or polytomous data regardless of sample size, missing data proportion, and asymmetry of item distributions. The discriminant analysis approach also performs well for dichotomous data. Naïvely rounding normal imputations or using logistic regression models to impute ordinal data are not recommended as they can potentially lead to substantial bias in all or some of the parameters.

KEYWORDS:

• missing data
• multiple imputation
• ordinal data

Notes

In saturated models, all nonredundant elements in the mean vector and covariance matrix are freely estimated.

An alternative way to identify the model is to fix one of the threshold parameters to be 0 and freely estimate the latent means.

In this case, the joint distribution of the continuous observed variables and latent variables underlying the ordinal variables is used for imputation. This joint distribution is often assumed to be multivariate normal.

Finch (2010) examined a stochastic regression imputation method in which ordinal missing data are predicted by a proportional odds logistic regression model (see Sulis & Porcu, 2008). He found that this approach provided comparable performance to the normal model approach with naïve rounding. However, the stochastic regression imputation is not directly comparable to the imputation done through an MCMC algorithm.