irtProb (version 1.0)

likelihoodCurve: Functions to Graph m4pl Likelihood Curves

Description

likelihoodCurve and groupLikelihoodCurve are used to graph the likelihood function curves according to the only theta, theta anc pseudo-guessing, theta and fluctuation, like theta and inattention m4pl models: only two simultaneous person parameters are taken in account.

Usage

likelihoodCurve(x, s, b, c, d,
                 limitT = c(min = -4, max = 4), limitS = c(min = 0, max = 4),
                 limitC = c(min = 0, max = 1), limitD = c(min = 0, max = 1),
                 grain         = 150, annotate = TRUE,
                 logLikelihood = FALSE, color = TRUE,
                 main          = "Likelihood Curve",
                 xlab          = expression(theta), ylab = NULL, zlab = "P(X)",
                 type          = "levelplot", m = 0)

 groupLikelihoodCurves(plotT, plotS, plotC, plotD, main=NULL, cex=0.7)

Arguments

x

numeric: binary (0,1) response pattern.

s

numeric: vector of inverse a discrimination item parameters.

b

numeric: vector of b difficulty item parameters.

c

numeric: vector of c pseudo-guessing item parameters.

d

numeric: vector of d inattention item parameters.

limitT

numeric: minimum and maximum of the proficiency person parameter used for the x axis.

limitS

numeric: minimum and maximum of the fluctuation person parameter used for the y axis.

limitC

numeric: minimum and maximum of the pseudo-guessing person parameter used for the y axis.

limitD

numeric: minimum and maximum of the inattention person parameter used for the y axis.

grain

numeric: number of theta values used to compute pattern distribution probability.

annotate

logical: does annotation is applied to the graphs?

logLikelihood

numeric: data.frame of the log likelihood of the studied models.

color

logical: does color is applied to contourplot or wireframe.

main

character: main title.

xlab

character: x axis label.

ylab

character: y axis label.

zlab

character: z axis label.

type

character: type of 3D plot ("levelplot", "contourplot" or "wireframe").

m

numeric: mean of the a priori probability distribution.

plotT

trellis: 2D theta likelihood curve.

plotS

trellis: 3D theta * S likelihood curve.

plotC

trellis: 3D theta * C likelihood curve.

plotD

trellis: 3D theta * D likelihood curve.

cex

numeric: zaxis label size.

Value

• likelihoodCurve
• plotT
  trellis: theta likelihood functions curves.
• plotS
  trellis: theta * S likelihood functions curves.
• plotC
  trellis: theta * C likelihood functions curves.
• plotD
  trellis: theta * D likelihood functions curves.
• parameters
  numeric: list of data.frame of person parameters for each model studied. Each element of the list shows estimation with different a priori probability distributions (uniform, normal and none).
• logLikelihood
  numeric: data.frame of the log likelihood for each model studied.
• groupLikelihoodCurves
• graphic
  graphic: all the likelihood functions curves are displayed.

Examples

## SIMULATION OF A RESPONSE PATTERN WITH 60 ITEMS
 nItems <- 60
 a      <- rep(1.702,nItems); b <- seq(-4,4,length=nItems)
 c      <- rep(0,nItems);     d <- rep(1,nItems)
 nSubjects <-  1
 theta     <-  -1
 S         <-  0.0
 C         <-  0.5
 D         <-  0.0
 
 set.seed(seed = 100)
 x         <- ggrm4pl(n=nItems, rep=1,
                      theta=theta, S=S, C=C, D=D,
                      s=1/a, b=b,c=c,d=d)

 ## Likelihood curves, person parameters estimates
  # and log likelihood of models graphed
 test <- likelihoodCurve(x=x, s=1/a, b=b, c=c, d=d, color=TRUE,
                         main="Likelihood Curve",
                         xlab=expression(theta), ylab=NULL, zlab="P(X)",
                         type="wireframe" , grain=50, limitD=c(0,1),
                         logLikelihood=FALSE, annotate=TRUE )

 # Contentd of the object test
 test$plotT
 test$plotC
 test$plotS
 test$plotD
 test$par
 round(test$logLikelihood,2)

 ## Graph of all the likelihood function curves
 groupLikelihoodCurves(test$plotT, test$plotS, test$plotC, test$plotD,
                       main=NULL, cex=0.7)