Weighting Imputation for Categorical Data

LVQ (Learning Vector Quantization) has been used to impute missing group membership and stratum weights in confirmatory factor analysis (CFA) model with continuous indicators (Chen, Tsai, & Yang, 2010; Tsai & Yang, 2012). Currently, categorical questionnaires (e.g., Binary and Likert-type items) are widely used in education, business, economy, and psychology tests as well as international large-scale surveys (e.g., Trend in International Mathematics and Science Study, TIMSS; Progress in International Reading Literacy Study, PIRLS; Program for International Students Assessment, PISA; German Survey of Income and Expenditure, SIE; British Labour Force Survey, LFS). This article aims to adapt the LVQ approach to assess the accuracy of parameters in a CFA model with missing background information in binary and Likert-type questionnaires through a series of simulations. Questionnaires utilizing categorical and binary items are widely used in business tests and largescale international surveys. In addition to the responses taken from the items included in the questionnaire, databases used for the analysis of questionnaire results also often provide weighting factors to compensate for non-response bias. This information can be utilized to produce estimates at the level of the population. However, weighting factors in such surveys are unable to consider all the background variables which may affect population level estimates. For example, in the LFS survey, the weight allocated to each individual to better ensure that the respondents were representative of the population was calculated based on age, sex, and region of residence alone (Office for National Statistics, 2011). However, while the researchers conducting the LFS were interested in the relationship between income and economic activity, the survey database did not provide a weighting factor for participant income. Without this weighting factor, a bias would have been introduced on account of the large number of subjects with missing incomes. This type of non-response bias is frequently encountered in the analysis of large-scale questionnaire data, however, to the best of our knowledge no method has been proposed in the literature to account for it. Therefore, to better compensate for this bias and provide more accurate population level estimates, the current study applied the LVQ method to calculate weighing factors for variables of interests. The concept of sampling weights and the practical applications of survey data have gradually gained importance in advanced statistical models (e.g., CFA, structural equation modeling, multilevel modeling; latent class analysis; latent growth model) (Asparouhov, 2005, 2006; Grilli & Pratesi, 2004; Kaplan & Ferguson, 1999; Patterson, Dayton, & Graubard, 2002; Stapleton, 2002, 2006, 2008; Sonnenschein, Stapleton, & Benson, 2010; Tsai & Yang, 2008; Yang & Tsai, 2006, 2008). To achieve effective results from the analysis of survey data, the analyst needs to adopt proper sampling weights for calculating paramLiang-Ting Tsai National Taichung University of Education, Taiwan