Frequentist and Bayesian approaches for comparing interviewer variance components in two groups of survey interviewers

Survey methodologists have long studied the effects of interviewers on the variance of survey estimates. Statistical models including random interviewer effects are often fitted in such investigations, and research interest lies in the magnitude of the interviewer variance component. One question that might arise in a methodological investigation is whether or not different groups of interviewers (e.g., those with prior experience on a given survey vs. new hires, or CAPI interviewers vs. CATI interviewers) have significantly different variance components in these models. Significant differences may indicate a need for additional training in particular subgroups, or sub-optimal properties of different modes or interviewing styles for particular survey items (in terms of the overall mean squared error of survey estimates). Survey researchers seeking answers to these types of questions have different statistical tools available to them. This paper aims to provide an overview of alternative frequentist and Bayesian approaches to the comparison of variance components in different groups of survey interviewers, using a hierarchical generalized linear modeling framework that accommodates a variety of different types of survey variables. We first consider the benefits and limitations of each approach, contrasting the methods used for estimation and inference. We next present a simulation study, empirically evaluating the ability of each approach to efficiently estimate differences in variance components. We then apply the two approaches to an analysis of real survey data collected in the U.S. National Survey of Family Growth (NSFG). We conclude that the two approaches tend to result in very similar inferences, and we provide suggestions for practice given some of the subtle differences observed.