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 analyse data collected under different designs (e.g., dual questioning, multilevel, mixed mode, repeated measurements designs, multiple-group designs). The well-known features of the GLM and GLMM (package lme4) software are remained, while adding new model-fit tests, residual analyses, and plot functions to give support to a profound RR data analysis. Data of Hoglinger and Jann (2018) and Hoglinger, Jann, and Diekmann (2014) is used to illustrate the methodology and software.
Highlights
Honest responding is encouraged by randomized response technique (RRT) by increasing anonymity and confidentiality
It can be shown that the maximum likelihood (ML) equations for the GLM for RR data resemble the general form of the GLM ML-equations (Fox et al, 2018, Appendix B)
Around 5% of the participants cheated in the roll-a-six game, and the estimates are comparable across RRT groups
Summary
Response distortion is known to be a potential threat to accurate (survey) results. The methodological literature shows many examples of misreporting of embarrassing or socially undesirable behaviors in surveys (Tourangeau and Yan, 2007; Tourangeau and Smith, 1996). The package rr of Blair et al (2015) was developed for univariate power analysis to measure the sensitive item prevalence for four RR designs It comprehends a logistic regression function for RR data collected with a single RR. Fox et al (2018) give an overview in which the RR-design parameters are represented as RR parameters for various RRTs. the RR designs work in different ways, a general RR model can be defined, which relates the RR data to the prevalence of the sensitive question. The RR designs work in different ways, a general RR model can be defined, which relates the RR data to the prevalence of the sensitive question This general RR model is extended to a GLM and GLMM by linking the prevalence πik to a linear predictor.
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