tam.fit.RdThe item infit and outfit statistic are calculated for
objects of classes tam, tam.mml and
tam.jml, respectively.
tam.fit(tamobj, ...) tam.mml.fit(tamobj, FitMatrix=NULL, Nsimul=NULL,progress=TRUE, useRcpp=TRUE, seed=NA, fit.facets=TRUE) tam.jml.fit(tamobj, trim_val=10) # S3 method for tam.fit summary(object, file=NULL, ...)
| tamobj | An object of class |
|---|---|
| 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 (<=1.1). |
| seed | Fixed simulation seed. |
| fit.facets | An optional logical indicating whether fit for all facet parameters should be computed. |
| trim_val | Optional trimming value. Squared standardized reaisuals
larger than |
| object | Object of class |
| file | Optional file name for summary output |
| ... | Further arguments to be passed |
In case of tam.mml.fit a data frame as entry itemfit
with four columns:
Item outfit statistic
The \(t\) value for the outfit statistic
Significance \(p\) value for outfit statistic
Significance \(p\) value for outfit statistic, adjusted for multiple testing according to the Holm procedure
Item infit statistic
The \(t\) value for the infit statistic
Significance \(p\) value for infit statistic
Significance \(p\) value for infit statistic, adjusted for multiple testing according to the Holm procedure
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. doi: 10.1007/978-0-387-49839-3_4
Fit statistics can be also calculated by the function msq.itemfit
which avoids simulations and directly evaluates individual
posterior distributions.
See tam.jml.fit for calculating item fit and person fit statistics
for models fitted with JML.
See tam.personfit for computing person fit statistics.
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).
############################################################################# # EXAMPLE 1: Dichotomous data data.sim.rasch ############################################################################# data(data.sim.rasch) # estimate Rasch model mod1 <- TAM::tam.mml(resp=data.sim.rasch) # item fit fit1 <- TAM::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 if (FALSE) { #-------- # infit and oufit based on estimated WLEs library(sirt) # estimate WLE wle <- TAM::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 ############################################################################# # 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::tam.mml( resp=dat, irtmodel="PCM2" ) summary(mod2) # estimate item fit fit2 <- TAM::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::tam.wle(mod2) # extract item parameters b1 <- - mod2$AXsi[, -1 ] # assess fit fit1a <- sirt::pcm.fit(b=b1, theta=wle$theta, dat) fit1a$item ############################################################################# # EXAMPLE 3: Fit statistic testing for local independence ############################################################################# # generate data with local dependence and User-defined fit statistics set.seed(4888) I <- 40 # 40 items N <- 1000 # 1000 persons delta <- seq(-2,2, len=I) theta <- stats::rnorm(N, 0, 1) # simulate data prob <- stats::plogis(outer(theta, delta, "-")) rand <- matrix( stats::runif(N*I), nrow=N, ncol=I) resp <- 1*(rand < prob) colnames(resp) <- paste("I", 1:I, sep="") #induce some local dependence for (item in c(10, 20, 30)){ # 20 #are made equal to the previous item row <- round( stats::runif(0.2*N)*N + 0.5) resp[row, item+1] <- resp[row, item] } #run TAM mod1 <- TAM::tam.mml(resp) #User-defined fit design matrix F <- array(0, dim=c(dim(mod1$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$A[,,33] fit <- TAM::tam.fit(mod1, FitMatrix=F) summary(fit) ############################################################################# # EXAMPLE 4: Fit statistic testing for items with differing slopes ############################################################################# #*** simulate data library(sirt) set.seed(9875) N <- 2000 I <- 20 b <- sample( seq( -2, 2, length=I ) ) a <- rep( 1, I ) # create some misfitting items a[c(1,3)] <- c(.5, 1.5 ) # simulate data dat <- sirt::sim.raschtype( rnorm(N), b=b, fixed.a=a ) #*** estimate Rasch model mod1 <- TAM::tam.mml(resp=dat) #*** assess item fit by infit and outfit statistic fit1 <- TAM::tam.fit( mod1 )$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 ) }