RRlin {RRreg}

Linear randomized response regression

Description

Linear regression for a continuous criterion, using randomized-response (RR) variables as predictors.

Usage

RRlin(
  formula,
  data,
  models,
  p.list,
  group = NULL,
  Kukrep = 1,
  bs.n = 0,
  nCPU = 1,
  maxit = 1000,
  fit.n = 3,
  pibeta = 0.05
)

Arguments

formula

a continuous criterion is predicted by one or more categorical RR variables defined by models. If the number of predictors exceeds the number defined by the vector models, the remaining predictors are treated as non-randomized variables (e.g., direct questions). Interactions including any of the RR variables cannot be included.

data

an optional data frame, list or environment, containing the variables in the model.

models

character vector specifying RR model(s) in order of appearance in formula. Available models: "Warner", "UQTknown", "UQTunknown", "Mangat", "Kuk", "FR", "Crosswise", "Triangular", "CDM", "CDMsym", "SLD", "custom" (custom: a randomization matrix must be specified in the corresponding element of p.list, where the entry p[i,j] defines the probability of responding i (i-th row) given a true state of j (j-th column)).

p.list

list of randomization probabilities for RR models in the same order as specified in models. Note, that the randomization probabilities p must be provided in a list, e.g., list(p=c(.2, .3)). See RRuni for details.

group

vector or matrix specifying group membership by the indices 1 and 2. Only for multigroup RR models, e.g., UQTunknown, CDM or SLD

Kukrep

defines the number of repetitions in Kuk's card playing method

bs.n

Number of samples used for the non-parametric bootstrap

nCPU

only relevant for the bootstrap: either the number of CPU cores or a cluster initialized via makeCluster.

maxit

maximum number of iterations in optimization routine

fit.n

number of fitting runs with random starting values

pibeta

approximate ratio of probabilities pi to regression weights beta (to adjust scaling). Can be used for speeding-up and fine-tuning ML estimation (i.e., choosing a smaller value for larger beta values).

Value

Returns an object RRlin which can be analysed by the generic method summary

Author(s)

Daniel W. Heck

References

van den Hout, A., & Kooiman, P. (2006). Estimating the linear regression model with categorical covariates subject to randomized response. Computational Statistics & Data Analysis, 50, 3311-3323.

See Also

vignette('RRreg') or https://www.dwheck.de/vignettes/RRreg.html for a detailed description of the RR models and the appropriate definition of p

Examples

# generate two RR predictors
dat <- RRgen(n = 500, pi = .4, model = "Warner", p = .3)
dat2 <- RRgen(n = 500, pi = c(.4, .6), model = "FR", p = c(.1, .15))
dat$FR <- dat2$response
dat$trueFR <- dat2$true

# generate a third predictor and continuous dependent variables
dat$nonRR <- rnorm(500, 5, 1)
dat$depvar <- 2 * dat$true - 3 * dat2$true +
  .5 * dat$nonRR + rnorm(500, 1, 7)

# use RRlin and compare to regression on non-RR variables
linreg <- RRlin(depvar ~ response + FR + nonRR,
  data = dat,
  models = c("Warner", "FR"),
  p.list = list(.3, c(.1, .15)), fit.n = 1
)
summary(linreg)
summary(lm(depvar ~ true + trueFR + nonRR, data = dat))