rasch.evm.pcm: Estimation of the Partial Credit Model using the Eigenvector...
In sirt: Supplementary Item Response Theory Models

rasch.evm.pcm

R Documentation

Estimation of the Partial Credit Model using the Eigenvector Method

Description

This function performs the eigenvector approach to estimate item parameters which is based on a pairwise estimation approach (Garner & Engelhard, 2002). No assumption about person parameters is required for item parameter estimation. Statistical inference is performed by Jackknifing. If a group identifier is provided, tests for differential item functioning are performed.

Usage

rasch.evm.pcm(dat, jackunits=20, weights=NULL, pid=NULL,
    group=NULL, powB=2, adj_eps=0.3, progress=TRUE )

## S3 method for class 'rasch.evm.pcm'
summary(object, digits=3, file=NULL, ...)

## S3 method for class 'rasch.evm.pcm'
coef(object,...)

## S3 method for class 'rasch.evm.pcm'
vcov(object,...)

Arguments

`dat`	Data frame with dichotomous or polytomous item responses
`jackunits`	A number of Jackknife units (if an integer is provided as the argument value) or a vector in which the Jackknife units are already defined.
`weights`	Optional vector of sample weights
`pid`	Optional vector of person identifiers
`group`	Optional vector of group identifiers. In this case, item parameters are group wise estimated and tests for differential item functioning are performed.
`powB`	Power created in `B` matrix which is the basis of parameter estimation
`adj_eps`	Adjustment parameter for person parameter estimation (see `mle.pcm.group`)
`progress`	An optional logical indicating whether progress should be displayed
`object`	Object of class `rasch.evm.pcm`
`digits`	Number of digits after decimals for rounding in `summary`.
`file`	Optional file name if `summary` should be sunk into a file.
`...`	Further arguments to be passed

Value

A list with following entries

`item`	Data frame with item parameters. The item parameter estimate is denoted by `est` while a Jackknife bias-corrected estimate is `est_jack`. The Jackknife standard error is `se`.
`b`	Item threshold parameters
`person`	Data frame with person parameters obtained (MLE)
`B`	Paired comparison matrix
`D`	Transformed paired comparison matrix
`coef`	Vector of estimated coefficients
`vcov`	Covariance matrix of estimated item parameters
`JJ`	Number of jackknife units
`JJadj`	Reduced number of jackknife units
`powB`	Used power of comparison matrix `B`
`maxK`	Maximum number of categories per item
`G`	Number of groups
`desc`	Some descriptives
`difstats`	Statistics for differential item functioning if `group` is provided as an argument

References

Choppin, B. (1985). A fully conditional estimation procedure for Rasch Model parameters. Evaluation in Education, 9, 29-42.

Garner, M., & Engelhard, G. J. (2002). An eigenvector method for estimating item parameters of the dichotomous and polytomous Rasch models. Journal of Applied Measurement, 3, 107-128.

Wang, J., & Engelhard, G. (2014). A pairwise algorithm in R for rater-mediated assessments. Rasch Measurement Transactions, 28(1), 1457-1459.

Examples

#############################################################################
# EXAMPLE 1: Dataset Liking for Science
#############################################################################

data(data.liking.science)
dat <- data.liking.science

# estimate partial credit model using 10 Jackknife units
mod1 <- sirt::rasch.evm.pcm( dat, jackunits=10 )
summary(mod1)

## Not run: 
# compare results with TAM
library(TAM)
mod2 <- TAM::tam.mml( dat )
r1 <- mod2$xsi$xsi
r1 <- r1 - mean(r1)
# item parameters are similar
dfr <- data.frame( "b_TAM"=r1, mod1$item[,c( "est","est_jack") ] )
round( dfr, 3 )
  ##      b_TAM    est est_jack
  ##  1  -2.496 -2.599   -2.511
  ##  2   0.687  0.824    1.030
  ##  3  -0.871 -0.975   -0.943
  ##  4  -0.360 -0.320   -0.131
  ##  5  -0.833 -0.970   -0.856
  ##  6   1.298  1.617    1.444
  ##  7   0.476  0.465    0.646
  ##  8   2.808  3.194    3.439
  ##  9   1.611  1.460    1.433
  ##  10  2.396  1.230    1.095
  ##  [...]

# partial credit model in eRm package
miceadds::library_install("eRm")
mod3 <- eRm::PCM(X=dat)
summary(mod3)
eRm::plotINFO(mod3)      # plot item and test information
eRm::plotICC(mod3)       # plot ICCs
eRm::plotPImap(mod3)     # plot person-item maps

#############################################################################
# EXAMPLE 2: Garner and Engelhard (2002) toy example dichotomous data
#############################################################################

dat <- scan()
   1 0 1 1   1 1 0 0   1 0 0 0   0 1 1 1   1 1 1 0
   1 1 0 1   1 1 1 1   1 0 1 0   1 1 1 1   1 1 0 0

dat <- matrix( dat, 10, 4, byrow=TRUE)
colnames(dat) <- paste0("I", 1:4 )

# estimate Rasch model with no jackknifing
mod1 <- sirt::rasch.evm.pcm( dat, jackunits=0 )

# paired comparison matrix
mod1$B
  ##          I1_Cat1 I2_Cat1 I3_Cat1 I4_Cat1
  ##  I1_Cat1       0       3       4       5
  ##  I2_Cat1       1       0       3       3
  ##  I3_Cat1       1       2       0       2
  ##  I4_Cat1       1       1       1       0

#############################################################################
# EXAMPLE 3: Garner and Engelhard (2002) toy example polytomous data
#############################################################################

dat <- scan()
   2 2 1 1 1   2 1 2 0 0   1 0 0 0 0   0 1 1 2 0   1 2 2 1 1
   2 2 0 2 1   2 2 1 1 0   1 0 1 0 0   2 1 2 2 2   2 1 0 0 1

dat <- matrix( dat, 10, 5, byrow=TRUE)
colnames(dat) <- paste0("I", 1:5 )

# estimate partial credit model with no jackknifing
mod1 <- sirt::rasch.evm.pcm( dat, jackunits=0, powB=3 )

# paired comparison matrix
mod1$B
  ##          I1_Cat1 I1_Cat2 I2_Cat1 I2_Cat2 I3_Cat1 I3_Cat2 I4_Cat1 I4_Cat2 I5_Cat1 I5_Cat2
  ##  I1_Cat1       0       0       2       0       1       1       2       1       2       1
  ##  I1_Cat2       0       0       0       3       2       2       2       2       2       3
  ##  I2_Cat1       1       0       0       0       1       1       2       0       2       1
  ##  I2_Cat2       0       1       0       0       1       2       0       3       1       3
  ##  I3_Cat1       1       1       1       1       0       0       1       2       3       1
  ##  I3_Cat2       0       1       0       2       0       0       1       1       1       1
  ##  I4_Cat1       0       1       0       0       0       2       0       0       1       2
  ##  I4_Cat2       1       0       0       2       1       1       0       0       1       1
  ##  I5_Cat1       0       1       0       1       2       1       1       2       0       0
  ##  I5_Cat2       0       0       0       1       0       0       0       0       0       0

#############################################################################
# EXAMPLE 4: Partial credit model for dataset data.mg from CDM package
#############################################################################

library(CDM)
data(data.mg,package="CDM")
dat <- data.mg[, paste0("I",1:11) ]

#*** Model 1: estimate partial credit model
mod1 <- sirt::rasch.evm.pcm( dat )
# item parameters
round( mod1$b, 3 )
  ##        Cat1   Cat2  Cat3
  ##  I1  -1.537     NA    NA
  ##  I2  -2.360     NA    NA
  ##  I3  -0.574     NA    NA
  ##  I4  -0.971 -2.086    NA
  ##  I5  -0.104  0.201    NA
  ##  I6   0.470  0.806    NA
  ##  I7  -1.027  0.756 1.969
  ##  I8   0.897     NA    NA
  ##  I9   0.766     NA    NA
  ##  I10  0.069     NA    NA
  ##  I11 -1.122  1.159 2.689

#*** Model 2: estimate PCM with pairwise package
miceadds::library_install("pairwise")
mod2 <- pairwise::pair(daten=dat)
summary(mod2)
plot(mod2)
# compute standard errors
semod2 <- pairwise::pairSE(daten=dat,  nsample=20)
semod2

#############################################################################
# EXAMPLE 5: Differential item functioning for dataset data.mg
#############################################################################

library(CDM)
data(data.mg,package="CDM")
dat <- data.mg[ data.mg$group %in% c(2,3,11), ]
# define items
items <- paste0("I",1:11)
# estimate model
mod1 <- sirt::rasch.evm.pcm( dat[,items], weights=dat$weight, group=dat$group )
summary(mod1)

#############################################################################
# EXAMPLE 6: Differential item functioning for Rasch model
#############################################################################

# simulate some data
set.seed(9776)
N <- 1000    # number of persons
I <- 10        # number of items
# simulate data for first group
b <- seq(-1.5,1.5,len=I)
dat1 <- sirt::sim.raschtype( stats::rnorm(N), b )
# simulate data for second group
b1 <- b
b1[4] <- b1[4] + .5 # introduce DIF for fourth item
dat2 <- sirt::sim.raschtype( stats::rnorm(N,mean=.3), b1 )
dat <- rbind(dat1, dat2 )
group <- rep( 1:2, each=N )
# estimate model
mod1 <- sirt::rasch.evm.pcm( dat, group=group )
summary(mod1)

## End(Not run)

sirt documentation built on Aug. 11, 2023, 5:07 p.m.