pcm.fit {sirt}

Item and Person Fit Statistics for the Partial Credit Model

Description

Computes item and person fit statistics in the partial credit model (Wright & Masters, 1990). The rating scale model is accommodated as a particular partial credit model (see Example 3).

Usage

pcm.fit(b, theta, dat)

Arguments

b

Matrix with item category parameters (see Examples)

theta

Vector with estimated person parameters

dat

Dataset with item responses

Value

A list with entries

itemfit

Item fit statistics

personfit

Person fit statistics

References

Wright, B. D., & Masters, G. N. (1990). Computation of outfit and infit statistics. Rasch Measurement Transactions, 3:4, 84-85.

See Also

See also personfit.stat for person fit statistics for dichotomous item responses. See also the PerFit package for further person fit statistics.

Item fit in other R packages: eRm::itemfit, TAM::tam.fit, mirt::itemfit, ltm::item.fit,

Person fit in other R packages: eRm::itemfit, mirt::itemfit, ltm::person.fit,

See pcm.conversion for conversions of different parametrizations of the partial credit model.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Partial credit model
#############################################################################

data(data.Students,package="CDM")
dat <- data.Students
# select items
items <- c(paste0("sc", 1:4 ), paste0("mj", 1:4 ) )
dat <- dat[,items]
dat <- dat[ rowSums( 1 - is.na(dat) ) > 0, ]

#*** Model 1a: Partial credit model in TAM
# estimate model
mod1a <- TAM::tam.mml( resp=dat )
summary(mod1a)
# estimate person parameters
wle1a <- TAM::tam.wle(mod1a)
# extract item parameters
b1 <- - mod1a$AXsi[, -1 ]
# parametrization in xsi parameters
b2 <- matrix( mod1a$xsi$xsi, ncol=3, byrow=TRUE )
# convert b2 to b1
b1b <- 0*b1
b1b[,1] <- b2[,1]
b1b[,2] <- rowSums( b2[,1:2] )
b1b[,3] <- rowSums( b2[,1:3] )
# assess fit
fit1a <- sirt::pcm.fit(b=b1, theta=wle1a$theta, dat)
fit1a$item

#############################################################################
# EXAMPLE 2: Rasch model
#############################################################################

data(data.read)
dat <- data.read

#*** Rasch model in TAM
# estimate model
mod <- TAM::tam.mml( resp=dat )
summary(mod)
# estimate person parameters
wle <- TAM::tam.wle(mod)
# extract item parameters
b1 <- - mod$AXsi[, -1 ]
# assess fit
fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, dat)
fit1a$item

#############################################################################
# EXAMPLE 3: Rating scale model
#############################################################################

data(data.Students,package="CDM")
dat <- data.Students
items <- paste0("sc", 1:4 )
dat <- dat[,items]
dat <- dat[ rowSums( 1 - is.na(dat) ) > 0, ]

#*** Model 1: Rating scale model in TAM
# estimate model
mod1 <- tam.mml( resp=dat, irtmodel="RSM")
summary(mod1)
# estimate person parameters
wle1 <- tam.wle(mod1)
# extract item parameters
b1 <- - mod1a$AXsi[, -1 ]
# fit statistic
pcm.fit(b=b1, theta=wle1$theta, dat)

## End(Not run)