Weighting Imputation for Categorical Data

Abstract

This article aims to propose the Learning Vector Quantization (LVQ) approach to impute missing group membership and sampling weights in inferring the accuracy of population parameters of confirmatory factor analysis (CFA) models with categorical questionnaires. Survey data with missing group memberships, for example, gender, age, or ethnicity, are very familiar. However, the group memberships of examinees are critical for calculating the stratum sampling weights. Asparouhov (2005), Tsai and Yang (2008), and Yang and Tsai (2008) have described that appropriate imputation can further improve the precision of CFA model estimations. Questionnaires with categorical responses are not well established yet. In this study, a Monte Carlo simulation was conducted to compare the LVQ method with the other three existing methods (e.g., listwise-deletion, weighting-class adjustment, non-weighted). Four experimental factors, such as missing data rates, sampling sizes, disproportionate sampling, and different populations, were used to examine the performance of these four methods. The results showed that the LVQ method outperformed the other three methods in terms of accuracy of parameters of CFA model with binary or 5-category responses. The conclusion and discussion sections of this article provide for some practical guidelines.