sgr (version 1.3.1)

pfakebad: Probability of faking bad.

Description

The function gives the conditional probability of replacement \(p(f=k|d=h,\theta_F)\) for discrete values in the range \(1, \ldots, Q\).

Usage

pfakebad(k, h = k, p = 0, Q = 5, gam = 1, del = 1)

Arguments

k

A fake value.

h

An observed original value.

p

Overall probability of replacement.

Q

Max value in the discrete r.v. range: \(1, \ldots, Q\).

gam

Gamma parameter.

del

Delta parameter.

Value

Gives the conditional probability based on the following equation $$ p(f=k|d=h,\theta_F)= \left\{ \begin{array}{cl} 1 & h=k=1 \\ GD(k;1,h-1,\gamma,\delta) \pi & 1 \leq k < h \leq Q \\ 1-\pi & 1 < h=k \leq Q \\ 0 & 1 \leq h < k \leq Q \end{array} \right. $$ with \(\theta_F\) and \(GD\) being the parameter vector \((\gamma,\delta,\pi)\) and the generalized Beta distribution for discrete variables (dgBetaD) with bounds \(a=h+1\) and \(b=Q\). The parameter \(\pi\) denotes the probability of faking bad.

References

Pastore, M., Lombardi, L. (2014). The impact of faking on Cronbach's Alpha for dichotomous and ordered rating scores. Quality & Quantity, 48, 1191-1211.

Examples

# NOT RUN {
x <- 1:7
GA <- c(1,3,1.5,8); DE <- c(1,3,4,2.5)
par(mfrow=c(2,2))
for (j in 1:4) {
  y <- NULL
  for (i in x) y <- c(y,pfakebad(x[i],h=5,Q=7,gam=GA[j],del=DE[j],p=.4))
  plot(x,y,type="h",panel.first=points(x,y,pch=19),
       main=paste("gamma=",GA[j]," delta=",DE[j],sep=""),ylim=c(0,.7),
       ylab="Replacement probability")  
}
# }