pfakegood: Probability of faking good.

In sgr: Sample Generation by Replacement

Probability of faking good.

Description

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

Usage

pfakegood(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, …, Q.
gam	Gamma parameter.
del	Delta parameter.

Value

Gives the conditional probability based on the following equation

p(f=k|d=h,θ_F)= ≤ft\{ \begin{array}{cl} 1 & h=k=Q \\ GD(k;h+1,Q,γ,δ) π & 1 ≤q h < k ≤q Q \\ 1-π & 1 ≤q k=h < Q \\ 0 & 1 ≤q k < h ≤q Q \end{array} \right.

with θ_F and GD being the parameter vector (γ,δ,π) and the generalized Beta distribution for discrete variables (dgBetaD) with bounds a=h+1 and b=Q. The parameter π denotes the probability of faking good.

Author(s)

Massimiliano Pastore & Luigi Lombardi

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

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,pfakegood(x[i],h=3,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")  
}

sgr documentation built on April 14, 2022, 5:08 p.m.