TAM (version 1.995-0)

tam.fit: Item Infit and Outfit Statistic

Description

The item infit and outfit statistic are calculated for objects of classes tam, tam.mml and tam.jml, respectively.

Usage

tam.fit(tamobj, ...)
tam.mml.fit(tamobj, FitMatrix=NULL, Nsimul=NULL,progress=TRUE, useRcpp=TRUE, seed=123, fit.facets=TRUE)
tam.jml.fit(tamobj)
"summary"(object, ...)

Arguments

tamobj

An object of class tam, tam.mml or tam.jml

FitMatrix

A fit matrix $F$ for a specific hypothesis of fit of the linear function $F \xi $ (see Simulated Example 3 and Adams & Wu 2007).

Nsimul

Number of simulations used for fit calculation. The default is 100 (less than 400 students), 40 (less than 1000 students), 15 (less than 3000 students) and 5 (more than 3000 students)

progress

An optional logical indicating whether computation progress should be displayed at console.

useRcpp

Optional logical indicating whether Rcpp or pure R code should be used for fit calculation. The latter is consistent with TAM (

seed

Fixed simulation seed.

fit.facets

An optional logical indicating whether fit for all facet parameters should be computed.

object

Object of class tam.fit

...

Further arguments to be passed

Value

In case of tam.mml.fit a data frame as entry itemfit with four columns:

Outfit

Item outfit statistic

Outfit_t

The $t$ value for the outfit statistic

Outfit_p

Significance $p$ value for outfit statistic

Outfit_pholm

Significance $p$ value for outfit statistic, adjusted for multiple testing according to the Holm procedure

Infit

Item infit statistic

Infit_t

The $t$ value for the infit statistic

Infit_p

Significance $p$ value for infit statistic

Infit_pholm

Significance $p$ value for infit statistic, adjusted for multiple testing according to the Holm procedure

Details

Item fit is automatically calculated in JML estimation using tam.jml.

References

Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model. A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.). Multivariate and mixture distribution Rasch models: Extensions and applications (pp. 55-76). New York: Springer.

See Also

Fit statistics can be also calculated by the function msq.itemfit which avoids simulations and directly evaluates individual posterior distributions. Item fit and person fit based on estimated person parameters can also be calculated using the sirt::pcm.fit function in the sirt package (see Example 1 and Example 2).

Examples

#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch
#############################################################################

data(data.sim.rasch)
# estimate Rasch model
mod1 <- tam.mml(resp=data.sim.rasch) 
# item fit
fit1 <- tam.fit( mod1 )
summary(fit1)
  ##   > summary(fit1)
  ##      parameter Outfit Outfit_t Outfit_p Infit Infit_t Infit_p
  ##   1         I1  0.966   -0.409    0.171 0.996  -0.087   0.233
  ##   2         I2  1.044    0.599    0.137 1.029   0.798   0.106
  ##   3         I3  1.022    0.330    0.185 1.012   0.366   0.179
  ##   4         I4  1.047    0.720    0.118 1.054   1.650   0.025

#--------
# infit and oufit based on estimated WLEs
library(sirt)

# estimate WLE
wle <- tam.wle(mod1)
# extract item parameters
b1 <- - mod1$AXsi[ , -1 ]
# assess item fit and person fit
fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta , data.sim.rasch )
fit1a$item       # item fit statistic
fit1a$person     # person fit statistic

## Not run: 
# #############################################################################
# # EXAMPLE 2: Partial credit model data.gpcm
# #############################################################################
# 
# data( data.gpcm )
# dat <- data.gpcm
# 
# # estimate partial credit model in ConQuest parametrization 'item+item*step'
# mod2 <- tam.mml( resp=dat , irtmodel="PCM2" )
# summary(mod2)
# # estimate item fit
# fit2 <- tam.fit(mod2)
# summary(fit2)
# 
# #  => The first three rows of the data frame correspond to the fit statistics
# #     of first three items Comfort, Work and Benefit.
# 
# #--------
# # infit and oufit based on estimated WLEs
# # compute WLEs
# wle <- tam.wle(mod2)
# # extract item parameters
# b1 <- - mod2$AXsi[ , -1 ]
# # assess fit
# fit1a <- sirt::pcm.fit(b=b1 , theta=wle$theta , dat)
# fit1a$item
# 
# #############################################################################
# # SIMULATED EXAMPLE 3: Fit statistic testing for local independence
# #############################################################################
# 
# #generate data with local DEPENDENCE and User-defined fit statistics
# set.seed(4888)
# I <- 40		# 40 items
# N <- 1000       # 1000 persons
# 
# delta <- seq(-2,2, len=I)
# theta <- stats::rnorm(N, 0, 1)
# # simulate data
# prob <- stats::plogis(outer(theta, delta, "-"))
# rand <- matrix( stats::runif(N*I), nrow=N, ncol=I)
# resp <- 1*(rand < prob)
# colnames(resp) <- paste("I" , 1:I, sep="")
#   
# #induce some local dependence
# for (item in c(10, 20, 30)){ 
#  #  20
#  #are made equal to the previous item 
#   row <- round( stats::runif(0.2*N)*N + 0.5)     
#   resp[row, item+1] <- resp[row, item]
# }
#   
# #run TAM
# mod1 <- tam.mml(resp)
#   
# #User-defined fit design matrix
# F <- array(0, dim=c(dim(mod1$A)[1], dim(mod1$A)[2], 6))
# F[,,1] <- mod1$A[,,10] + mod1$A[,,11]
# F[,,2] <- mod1$A[,,12] + mod1$A[,,13]
# F[,,3] <- mod1$A[,,20] + mod1$A[,,21]
# F[,,4] <- mod1$A[,,22] + mod1$A[,,23]
# F[,,5] <- mod1$A[,,30] + mod1$A[,,31]
# F[,,6] <- mod1$A[,,32] + mod1$A[,,33]
# fit <- tam.fit(mod1, FitMatrix=F)
# summary(fit)
# 
# #############################################################################
# # SIMULATED EXAMPLE 4: Fit statistic testing for items with differing slopes
# #############################################################################
# 
# #*** simulate data
# library(sirt)
# set.seed(9875)
# N <- 2000
# I <- 20
# b <- sample( seq( -2 , 2 , length=I ) )
# a <- rep( 1, I )
# # create some misfitting items
# a[c(1,3)] <- c(.5 , 1.5 )
# # simulate data
# dat <- sirt::sim.raschtype( rnorm(N) , b=b , fixed.a=a )
# #*** estimate Rasch model
# mod1 <- tam.mml(resp=dat) 
# #*** assess item fit by infit and outfit statistic
# fit1 <- tam.fit( mod1 )$itemfit
# round( cbind( "b"=mod1$item$AXsi_.Cat1 , fit1$itemfit[,-1] )[1:7,], 3 )  
# 
# #*** compute item fit statistic in mirt package
# library(mirt)
# library(sirt)
# mod1c <- mirt::mirt( dat , model=1 , itemtype="Rasch" , verbose=TRUE)
# print(mod1c)                      # model summary
# sirt::mirt.wrapper.coef(mod1c)    # estimated parameters
# fit1c <- mirt::itemfit(mod1c , method="EAP")    # model fit in mirt package
# # compare results of TAM and mirt
# dfr <- cbind( "TAM"=fit1 , "mirt"=fit1c[,-c(1:2)] )
# 
# # S-X2 item fit statistic (see also the output from mirt) 
# library(CDM)
# sx2mod1 <- CDM::itemfit.sx2( mod1 )
# summary(sx2mod1)
# 
# # compare results of CDM and mirt
# sx2comp <-  cbind( sx2mod1$itemfit.stat[ , c("S-X2" , "p") ]  , 
#                     dfr[  , c("mirt.S_X2" , "mirt.p.S_X2") ] )
# round(sx2comp , 3 )
# ## End(Not run)