# Mixed Effects Logistic Regression for RR Data Uses the package `lme4` to fit a generalized linear mixed model (GLMM) with an adjusted link funciton. ```r RRmixed(formula, data, model, p, const = 1e-04, adjust_control = FALSE, ...) ``` ## Arguments - `formula`: two-sided formula including random and fixed effects (see below or `glmer` for details) - `data`: an optional data frame with variables named in formula - `model`: type of RR design. Only 1-group RR designs are supported at the moment (i.e., `"Warner"`, `"FR"`, `"UQTknown"`, `"Crosswise"`, `"Triangular"`, `"Kuk"`, `"Mangat"`, `"custom"`). See `RRuni` or `vignette(RRreg)` for details. - `p`: randomization probability - `const`: the RR link function is not defined for small and/or large probabilities (the boundaries depend on `model` and `p`). To increase robustness of the estimation, these probabilities smaller and larger than the respective boundaries (plus/minus a constant defined via `const`) are smoothed by separate logit-link functions. - `adjust_control`: whether to adjust the control arguments for `glmer`, which might help in case of convergence issues for some models. `lmerControl` settings are changed to `nAGQ0initStep = FALSE` and `optimizer = "bobyqa"`. - `...`: further arguments passed to `glmer` ## Returns an object of class `glmerMod` ## Details Some examples for formula: * random intercept: `response ~ covariate + (1 | group)` * random slope: `response ~ covariate + (0 + covariate | group)` * both random slope and intercept: `response ~ covariate +(covariate | group)` * level-2 predictor (must have constant values within groups!): `response ~ lev2 + (1|group)` Note that parameter estimation will be unstable and might fail if the observed responses are not in line with the model. For instance, a Forced-Response model (`model="FR"`) with `p=c(0,1/4)` requires that expected probabilities for responses are in the interval [.25,1.00]. If the observed proportion of responses is very low (<<.25), intercepts will be estimated to be very small (<<0) and/or parameter estimation might fail. See `glmer` for setting better starting values and `lmerControl` for further options to increase stability. ## Examples ```r # generate data with a level-1 predictor set.seed(1234) d <- data.frame( group = factor(rep(LETTERS[1:20], each = 50)), cov = rnorm(20 * 50) ) # generate dependent data based on logistic model (random intercept): d$true <- simulate(~ cov + (1 | group), newdata = d, family = binomial(link = "logit"), newparams = list( beta = c("(Intercept)" = -.5, cov = 1), theta = c("group.(Intercept)" = .8) ) )[[1]] # scramble responses using RR: model <- "FR" p <- c(true0 = .1, true1 = .2) d$resp <- RRgen(model = "FR", p = p, trueState = d$true)$response # fit model: mod <- RRmixed(resp ~ cov + (1 | group), data = d, model = "FR", p = p) summary(mod) ``` ## References van den Hout, A., van der Heijden, P. G., & Gilchrist, R. (2007). The Logistic Regression Model with Response Variables Subject to Randomized Response. Computational Statistics & Data Analysis, 51, 6060–6069.

RRmixed function