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The randomized response (RR) technique was developed to improve the validity of measures assessing attitudes, behaviors, and attributes threatened by social desirability bias. The RR removes any direct link between individual responses and the sensitive attribute to maximize the anonymity of respondents and, in turn, to elicit more honest responding. Since multivariate analyses are no longer feasible using standard methods, we present the R package RRreg that allows for multivariate analyses of RR data in a user-friendly way. We show how to compute bivariate correlations, how to predict an RR variable in an adapted logistic regression framework (with or without random effects), and how to use RR predictors in a modified linear regression. In addition, the package allows for power analysis and robustness simulations. To facilitate the application of these methods, we illustrate the benefits of multivariate methods for RR variables using an empirical example.