sirt (version 1.5-0)

pcm.fit: 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 accomodated 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 Rpackages: itemfit (eRm), tam.fit (TAM), itemfit (mirt), item.fit (ltm), Person fit in other Rpackages: itemfit (eRm), itemfit (mirt), person.fit (ltm), See pcm.conversion for conversions of different parametrizations of the partial credit model.

Examples

#############################################################################
# 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$xsi , ncol=3 , byrow=TRUE )
# convert b2 to b1
b1b <- 0*b1
b1b[,1] <- b2[,1]
b1b[,2] <- rowSums( b2[,1:2] )
b1b[,3] <- rowSums( b2[,1:3] )
# assess fit
fit1a <- pcm.fit(b=b1, theta=wle1a$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$AXsi[ , -1 ]
# assess fit
fit1a <- pcm.fit(b=b1, theta=wle$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)