RRreg (version 0.7.5)

RRmixed: Mixed Effects Logistic Regression for RR Data

Description

Uses the package lme4 to fit a generalized linear mixed model (GLMM) with an adjusted link funciton.

Usage

RRmixed(formula, data, model, p, const = 1e-04, adjust_control = FALSE, ...)

Value

an object of class glmerMod

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

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.

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.

Examples

# 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)