RRglmer: Fitting Generalized Linear Mixed-Effects Models with binary...

In GLMMRR: Generalized Linear Mixed Model (GLMM) for Binary Randomized Response Data

Description

Fit a generalized linear mixed-effects model (GLMM) with binary Randomized Response data. Both fixed effects and random effects are specified via the model formula. Randomize response parameters can be entered either as single values or as vectors. Implemented as a wrapper for glmer. Reference: Fox, J-P, Veen, D. and Klotzke, K. (2018). Generalized Linear Mixed Models for Randomized Responses. Methodology. https://doi.org/10.1027/1614-2241/a000153

Usage

RRglmer(
  formula,
  item,
  link,
  RRmodel,
  p1,
  p2,
  data,
  control = glmerControl(),
  na.action = "na.omit",
  ...
)

Arguments

formula	a two-sided linear formula object describing both the fixed-effects and fixed-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expressions for design matrices from grouping factors.
item	optional item identifier for long-format data.
link	a glm link function for binary outcomes. Must be a function name. Available options: "RRlink.logit", "RRlink.probit", "RRlink.cloglog" and "RRlink.cauchit"
RRmodel	the Randomized Response model, defined per case. Available options: "DQ", "Warner", "Forced", "UQM", "Crosswise", "Triangular" and "Kuk"
p1	the Randomized Response parameter p1, defined per case. Must be 0 <= p1 <= 1.
p2	the Randomized Response parameter p2, defined per case. Must be 0 <= p2 <= 1.
data	a data frame containing the variables named in formula as well as the Randomized Response model and parameters. If the required information cannot be found in the data frame, or if no data frame is given, then the variables are taken from the environment from which RRglmer is called.
control	a list (of correct class, resulting from lmerControl() or glmerControl() respectively) containing control parameters, including the nonlinear optimizer to be used and parameters to be passed through to the nonlinear optimizer, see the *lmerControl documentation for details.
na.action	a function that indicates what should happen when the data contain NAs. The default action (na.omit, as given by getOption("na.action"))) strips any observations with any missing values in any variables.
...	other potential arguments to be passed to glmer.

Value

An object of class RRglmerMod. Extends the class glmerMod with Randomize Response data, for which many methods are available (e.g. methods(class="glmerMod")).

See Also

lme4

Examples

# Fit the model with fixed effects for gender, RR and pp
# and a random effect for age using the logit link function.
# The Randomized Response parameters p1, p2 and model
# are specified for each observation in the dataset.
out <- RRglmer(response ~ Gender + RR + pp + (1|age), link="RRlink.logit", RRmodel=RRmodel,
         p1=RRp1, p2=RRp2, data=Plagiarism, na.action = "na.omit",
         etastart = rep(0.01, nrow(Plagiarism)),
         control = glmerControl(optimizer = "Nelder_Mead", tolPwrss = 1e-03), nAGQ = 1)
summary(out)

Example output

Loading required package: lme4
Loading required package: Matrix
RRglmer(formula = "response~Gender+RR+pp+age", link = "RRlink.logit", 
    RRmodel = RRmodel, p1 = RRp1, p2 = RRp2, data = Plagiarism, 
    control = glmerControl(optimizer = "Nelder_Mead", tolPwrss = 0.001), 
    na.action = "na.omit", ... = pairlist(etastart = rep(0.01, 
        nrow(Plagiarism)), nAGQ = 1))
Generalized linear mixed model fit by maximum likelihood (Laplace
  Approximation) [glmerMod]
 Family: binomial  ( RRlogit )
Formula: response ~ Gender + RR + pp + (1 | age)
   Data: df
Control: 
structure(list(optimizer = c("Nelder_Mead", "Nelder_Mead"), calc.derivs = TRUE,  
    use.last.params = FALSE, restart_edge = FALSE, boundary.tol = 1e-05,  
    tolPwrss = 0.001, compDev = TRUE, nAGQ0initStep = TRUE, checkControl = structure(list( 
        check.nobs.vs.rankZ = "ignore", check.nobs.vs.nlev = "stop",  
        check.nlev.gtreq.5 = "ignore", check.nlev.gtr.1 = "stop",  
        check.nobs.vs.nRE = "stop", check.rankX = "message+drop.cols",  
        check.scaleX = "warning", check.formula.LHS = "stop",  
        check.response.not.const = "stop"), .Names = c("check.nobs.vs.rankZ",  
    "check.nobs.vs.nlev", "check.nlev.gtreq.5", "check.nlev.gtr.1",  
    "check.nobs.vs.nRE", "check.rankX", "check.scaleX", "check.formula.LHS",  
    "check.response.not.const")), checkConv = structure(list( 
        check.conv.grad = structure(list(action = "warning",  
            tol = 0.001, relTol = NULL), .Names = c("action",  
        "tol", "relTol")), check.conv.singular = structure(list( 
            action = "message", tol = 1e-04), .Names = c("action",  
        "tol")), check.conv.hess = structure(list(action = "warning",  
            tol = 1e-06), .Names = c("action", "tol"))), .Names = c("check.conv.grad",  
    "check.conv.singular", "check.conv.hess")), optCtrl = list()), .Names = c("optimizer",  
"calc.derivs", "use.last.params", "restart_edge", "boundary.tol",  
"tolPwrss", "compDev", "nAGQ0initStep", "checkControl", "checkConv",  
"optCtrl"), class = c("glmerControl", "merControl"))

     AIC      BIC   logLik deviance df.resid 
   816.3    839.7   -403.1    806.3      797 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.6814 -0.3004  0.5965  0.7068 10.2851 

Random effects:
 Groups Name        Variance Std.Dev.
 age    (Intercept) 0.1367   0.3697  
Number of obs: 802, groups:  age, 20

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -4.9643     1.0004  -4.962 6.97e-07 ***
Gender        0.1016     0.5177   0.196  0.84437    
RR            1.3503     0.5088   2.654  0.00796 ** 
pp            2.1542     0.9203   2.341  0.01924 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
       (Intr) Gender RR    
Gender -0.326              
RR     -0.213  0.012       
pp     -0.845  0.081 -0.110

### GLMMRR - Binary Randomized Response Data ###
Generalized linear mixed-effects model

Family:			 binomial 
Link function:		 RRlogit 

---------------------------------------------------------
Item:			 Single item 
Model(s):		 Crosswise (0.25 | 0) 
			 DQ (1.00 | 0) 

## Estimated Population Prevalence (weighted per RR model) 
   RRmodel estimate.weighted se.weighted   n
 Crosswise          0.115635    0.037257 614
        DQ          0.037234    0.013809 188

GLMMRR documentation built on Jan. 16, 2021, 5:28 p.m.