Generalized Linear Mixed Models for Randomized Responses

Abstract

Response bias (nonresponse and social desirability bias) is one of the main concerns when asking sensitive questions about behavior and attitudes. Self-reports on sensitive issues as in health research (e.g., drug and alcohol abuse), and social and behavioral sciences (e.g., attitudes against refugees, academic cheating) can be expected to be subject to considerable misreporting. To diminish misreporting on self-reports, indirect questioning techniques have been proposed such as the randomized response techniques. The randomized response techniques avoid a direct link between individual's response and the sensitive question, thereby protecting the individual's privacy. Next to the development of the innovative data collection methods, methodological advances have been made to enable a multivariate analysis to relate responses to sensitive questions to other variables. It is shown that the developments can be represented by a general response probability model (including all common designs) by extending it to a generalized linear model (GLM) or a generalized linear mixed model (GLMM). The general methodology is based on modifying common link functions to relate a linear predictor to the randomized response. This approach makes it possible to use existing software for GLMs and GLMMs to model randomized response data. The R-package GLMMRR makes the advanced methodology available to applied researchers. The extended models and software will seriously improve the application of the randomized response methodology. Three empirical examples are given to illustrate the methods.