Generalized Linear Randomized Response Modeling using GLMMRR

Abstract

Randomized response (RR) designs are used to collect response data about sensitive behaviors (e.g., criminal behavior, sexual desires). The modeling of RR data is more complex since it requires a description of the RR process. For the class of generalized linear mixed models (GLMMs), the RR process can be represented by an adjusted link function, which relates the expected RR to the linear predictor for most common RR designs. The package GLMMRR includes modified link functions for four different cumulative distributions (i.e., logistic, cumulative normal, Gumbel, Cauchy) for GLMs and GLMMs, where the package lme4 facilitates ML and REML estimation. The mixed modeling framework in GLMMRR can be used to jointly analyze data collected under different designs (e.g., dual questioning, multilevel, mixed mode, repeated measurements designs, multiple-group designs). Model-fit tests, tools for residual analyses, and plot functions to give support to a profound RR data analysis are added to the well-known features of the GLM and GLMM software (package lme4). Data of Höglinger and Jann (2018) and Höglinger, Jann, and Diekmann (2014) are used to illustrate the methodology and software.