RRreg (version 0.7.5)

RRsimu: Monte Carlo simulation for one or two RR variables

Description

Simulate and analyse bivariate data including either one RR variable (either correlation, logistic, or linear regression model) or two RR variables (only correlations). Useful for power analysis, parametric bootstraps or for testing the effects of noncompliance on the stability of estimates.

Usage

RRsimu(
  numRep,
  n,
  pi,
  model,
  p,
  cor = 0,
  b.log = 0,
  complyRates = c(1, 1),
  sysBias = c(0, 0),
  method = c("RRuni", "RRcor", "RRlog", "RRlin"),
  alpha = 0.05,
  groupRatio = 0.5,
  MLest = FALSE,
  getPower = TRUE,
  nCPU = 1
)

Value

A list containing

parEsts

matrix containing the estimated parameters

results

matrix with mean parameters, standard errors, and number of samples to which the respective method could not be fitted

power

vector with the estimated power of the selected randomized response procedures

Arguments

numRep

number of replications

n

sample size

pi

true proportion of carriers of sensitive attribute (for 2 RR variables: vector)

model

either one or two RR model (as vector), see RRuni

p

randomization probability (for 2 RR variables: a list). See RRuni for details.

cor

true Pearson-correlation used for data generation (for RRcor). Can also be used to generate data with two dichotomous RR variables.

b.log

true regression coefficient in logistic regression (for RRlog)

complyRates

vector with two values giving the proportions of participants who adhere to the instructions in the subset with or without the sensitive attribute, respectively (for 2 RR variables: a list)

sysBias

probability of responding 'yes' (coded as 1 in the RR variable) in case of non-compliance for carriers and non-carriers, respectively. See RRgen

method

vector specifying which RR methods to be used in each replication. For a single RR variable, the methods RRuni, RRcor,RRlog, and RRlin are available. For 2 RR variables, only RRcor is available.

alpha

significance threshold for testing the logistic regression parameter beta

groupRatio

proportion of participants in group 1. Only for two-group models (e.g., "SLD") (for 2 RR variables: vector)

MLest

concerns RRuni: whether to use optim to get ML instead of moment estimates (only relevant if pi is outside of [0,1])

getPower

whether to compute power for method="RRcor" (performs an additional bootstrap assuming independence)

nCPU

either the number of CPU cores or a cluster initialized via makeCluster.

Details

For a single RR variable:

The parameter b.log is the slope-coefficient for the true, latent values in a logistic regression model that is used for data generation.

The argument cor is used for data generation for linear models. The directly measured covariate is sampled from a normal distribution with shifted means, depending on the true state on the sensitive attribute (i.e., the true, underlying values on the RR variable). For dichotomous RR variables, this corresponds to the assumption of an ordinary t-test, where the dependent variable is normally distributed within groups with equal variance. The difference in means is chosen in a way, to obtain the point-biserial correlation defined by cor.

For two RR variables:

cor has to be used. In case of two dichotomous RR variables, the true group membership of individuals is sampled from a 2x2 cross table. Within this table, probabilities are chosen in a way, to obtain the point-tetrachoric correlation defined by cor

Note, that for the FR model with multiple response categories (e.g., from 0 to 4), the specified cor is not the exact target of the sampling procedure. It assumes a normal distribution for each true state, with constant differences between the groups (i.e., it assumes an interval scaled variable).

Examples

# Not run: Simulate data according to the Warner model
# mcsim <-  RRsimu(numRep=100, n=300, pi=.4,
#                  model="Warner", p=.2, cor=.3)
# print(mcsim)