Using R Software for Rasch Model Calibrations

Abstract

This chapter provides an overview of the open-source, freely available R software and introduces Rasch item response modeling programs in R for unidimensional and multidimensional data which are dichotomously or polytomously scored. An introduction provides instructions for installing the software, writing and executing syntax in the R console, and loading packages. The “eRm” package is utilized for performing the simple Rasch analysis for unidimensional, dichotomous data. The “TAM” package is used for illustrating the Partial Credit Model (Masters, Psychometrika, 47, 149–174, 1982) for unidimensional, polytomous data. The “mirt” package is utilized for performing between-item multidimensional Rasch analysis for dichotomous data.

Appendices

Epilogue

The purpose of this chapter is the introduction of R Rasch family modeling via “eRm”, “TAM”, and “mirt”. As such it is not possible to cover wider ranges of functions in these packages. For those who want to pursue learning more about the R item response modeling, authors (Paek & Cole, 2020) have written a detailed book, Using R for Item Response Theory Model Applications, that describes further details of Rasch family modeling in R and multidimensional modeling using R. In addition to learning how to use R Rasch model programs, the study of the Rasch models through a course or article/book reading (e.g., Wilson, 2005) is also strongly recommended.

R Code

1+1	#0.1
sqrt(4)	#0.2
help(sqrt)	#0.3
?sqrt	#0.4
setwd(“C:/workingdirectory”)	#0.5
read.table(“Rdata1.csv”, sep=“,”, header=TRUE)	#0.6
install.packages(“eRm”)	#0.7
install.packages(“TAM”)	#0.8
install.packages(“mirt”)	#0.9
Unidimensional Rasch Application for Dichotomous Data (using the “eRm” package)
library(eRm)	#1.1
data1 <- raschdat3	#1.2
head(data1)	#1.3
dim(data1)	#1.4
names(data1)	#1.5
mod.rm <- RM(data1)	#1.6
mod.rm$conv	#1.7
-mod.rm$betapar	#1.8
mod.rm$se.beta	#1.9
summary(mod.rm)	#1.10
plotICC(mod.rm)	#1.11
plotICC(mod.rm, 1:3)	#1.12
plotICC(mod.rm, item.subset=c(1,3,5))	#1.13
dev.off(dev.list()[“RStudioGD”])	#1.14
p.rm <- person.parameter(mod.rm)	#1.15
p.rm	#1.16
plot(p.rm)	#1.17
plotPImap(mod.rm)	#1.18
install.packages(“WrightMap”)	#1.19
library(WrightMap)	#1.20
WrightMap(as.matrix(p.rm$thetapar$NAgroup1),-mod.rm$betapar)	#1.21
rm.lrt <- LRtest(mod.rm)	#1.22
rm.lrt	#1.23
Waldtest(mod.rm)	#1.24
itemfit(p.rm)	#1.25
detach(“package:eRm”)	#1.26
Unidimensional Rasch Application for Polytomous Data (using “ TAM ” for PCM )
library(TAM)	#2.1
data(data.gpcm)	#2.2
data2 <- data.gpcm	#2.3
head(data2)	#2.4
dim(data2)	#2.5
names(data2)	#2.6
mod.pcm <- tam.mml(data2, irtmodel="PCM")	#2.7
mod.pcm$xsi	#2.8
round(mod.pcm$xsi,3)	#2.9
plot(mod.pcm, items=1, type=“items”, export=FALSE)	#2.10
plot(mod.pcm, items=2, type=“items”, export=FALSE)	#2.11
plot(mod.pcm, items=3, type=“items”, export=FALSE)	#2.12
p.pcm <- mod.pcm$person	#2.13
head(p.pcm)	#2.14
p.pcm.wle <- tam.wle(mod.pcm)	#2.15
p.pcm.theta <- p.pcm.wle$theta	#2.16
head(p.pcm.theta)	#2.17
tam.fit(mod.pcm)$itemfit	#2.18
summary(mod.pcm)	#2.19
detach(“package:TAM”)	#2.20
Multidimensional Rasch Application for Dichotomous Data (using “mirt”)
library(mirt)	#3.1
L6 <- expand.table(LSAT6)	#3.2
L7 <- expand.table(LSAT7)	#3.3
set.seed(111)	#3.4
data3 <- cbind(L6[sample(nrow(L6),300),],L7[sample(nrow(L7),300),])	#3.5
head(data3)	#3.6
dim(data3)	#3.7
names(data3)	#3.8
spec <- “F1 = 1−5  F2 = 6−10  COV = F1*F2”	#3.9
mod.md <- mirt(data3, model=spec, itemtype=“Rasch”, SE=TRUE)	#3.10
mod.md	#3.11
coef(mod.md, simplify=TRUE)	#3.12
coef(mod.md, printSE=TRUE)	#3.13
itemplot(mod.md, 1)	#3.14
itemplot(mod.md, 1, type=“info”)	#3.15
p.md <- fscores(mod.md, method=“EAP”, full.scores=FALSE)	#3.16
p.md <- fscores(mod.md, method=“EAP”, full.scores=TRUE, full.scores.SE=TRUE)	#3.17
head(p.md)	#3.18
M2(mod.md)	#3.19
itemfit(mod.md, fit_stats = “infit”)	#3.20
detach(“package:mirt”)	#3.21