RaschInt: Scoring Methods to Change Observed Scores

In vthorrf/CIRM: Procedures for IRT modeling

Description

Creates a ordered matrix to be evaluated using Additive Conjoint Measurement Theory.

Usage

scoring(rabil,rdiff,n,v,x,l,p=.5,type="rank")

Arguments

rabil	A vector of estimates of person abilities.
rdiff	A vector of estimates of item difficulty.
n	The number of individuals in the sample.
v	The number of items in the test.
x	A long format dataset. Only used for type "bayes".
l	The number of levels on the scale. Only used for type "bayes".
p	The probability of answering right when ability and difficulty match. Used for types "cond" and "condb".
type	The method of scoring. "rank" if the ranking method is prefered. "cond" if conditional probability method is prefered. "bayes" if Bayesian Rasch method is prefered. "condb" if Bayesian Conditional is prefered. "2PL" if Two-parameter logistic is prefered.

Value

A list containing the following component (for "rank" and "cond" methods):

scores

A rescored data set.

For "bayes", "condb" and "2PL" methods:

matrix	A rescored data set.
abil	Aptitude estimates.
easi	Easiness estimates.
dic	DIC fit.
full	The full Bayesian run.

For "2PL" method:

matrix	A rescored data set.
abil	Aptitude estimates.
easi	Easiness estimates.
disc	Discrimination estimates.
dic	DIC fit.
full	The full Bayesian run.

Examples

### Random Data with 100 observations and 10 variables with 5 levels of response
n = 100; v = 10; l = 5
Data <- matrix(NA,nrow=n,ncol=v)
psi <- seq(length=n,-3,3); theta <- seq(length=v,-3,3); eta <- matrix(NA,ncol=v,nrow=n)
seed <- matrix(c(1:(n*v)),nrow=n,ncol=v)
for(i in 1:n)
{
  for(j in 1:v)
  {
    set.seed(seed[i,j])
    eta[i,j] <- exp(psi[i]-theta[j])/(1+exp(psi[i]-theta[j]))
    Data[i,j] <- rbinom(1,l-1,eta[i,j])
  }
}
rm(eta,seed,i,j)
Subj1 <- vector(mode="character",length=9); Subj2 <- vector(mode="character",length=n)
Item <- vector(mode="character",length=v)
for (i in 1:9) {Subj1[i] <- paste("S",0,i,sep="")}
for (i in 1:n) {Subj2[i] <- paste("S",i,sep="")}; Subj2 <- Subj2[10:n]
Subj <- c(Subj1,Subj2); rm(Subj1,Subj2)
for (i in 1:v) {Item[i] <- paste("I",i,sep="")}
DF <- data.frame(Subj,Data); colnames(DF) <- c("Subj",Item[1:v])
require(tidyr)
theData <- gather(DF, Subj, Correct, I1:I10, factor_key=TRUE)
colnames(theData) <- c("Subj","Item","Correct")
theData <- theData[with(theData, order(Subj)), ]
rownames(theData) <- c(1:(n*v)); head(theData)
theData$Subj = factor( theData$Subj )
theData$Item = factor( theData$Item )
theData$Correct = as.integer( theData$Correct )

### Create Scores
AbilF <- latent.vs(Data,l,what="person",method="freq")
Af <- AbilF$abil
EasiF <- latent.vs(Data,l,what="item",method="freq")
Ef <- EasiF$easi

### Rescore
scoring(n=n,v=v,type="rank")
scoring(rabil=Af,rdiff=1-Ef,type="cond")
scoring(n=n,v=v,x=theData,l=l,type="bayes")
scoring(n=n,v=v,x=theData,l=l,type="condb")
scoring(n=n,v=v,x=theData,l=l,type="2PL")

vthorrf/CIRM documentation built on Nov. 5, 2019, 12:05 p.m.