sirt (version 1.14-0)

data.long: Longitudinal Dataset

Description

This dataset contains 200 observations on 12 items. 6 items (I1T1, ... ,I6T1) were administered at measurement occasion T1 and 6 items at T2 (I3T2, ... , I8T2). There were 4 anchor items which were presented at both time points. The first column in the dataset contains the student identifier.

Usage

data(data.long)

Format

The format of the dataset is 'data.frame': 200 obs. of 13 variables: $ idstud: int 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 ... $ I1T1 : int 1 1 1 1 1 1 1 0 1 1 ... $ I2T1 : int 0 0 1 1 1 1 0 1 1 1 ... $ I3T1 : int 1 0 1 1 0 1 0 0 0 0 ... $ I4T1 : int 1 0 0 1 0 0 0 0 1 1 ... $ I5T1 : int 1 0 0 1 0 0 0 0 1 0 ... $ I6T1 : int 1 0 0 0 0 0 0 0 0 0 ... $ I3T2 : int 1 1 0 0 1 1 1 1 0 1 ... $ I4T2 : int 1 1 0 0 1 1 0 0 0 1 ... $ I5T2 : int 1 0 1 1 1 1 1 0 1 1 ... $ I6T2 : int 1 1 0 0 0 0 0 0 0 1 ... $ I7T2 : int 1 0 0 0 0 0 0 0 0 1 ... $ I8T2 : int 0 0 0 0 1 0 0 0 0 0 ...

Examples

## Not run: 
# data(data.long)
# dat <- data.long
# dat <- dat[,-1]
# I <- ncol(dat)
# 
# #*************************************************
# # Model 1: 2-dimensional Rasch model
# #*************************************************
# # define Q-matrix
# Q <- matrix(0,I,2)
# Q[1:6,1] <- 1
# Q[7:12,2] <- 1
# rownames(Q) <- colnames(dat)
# colnames(Q) <- c("T1","T2")
# 
# # vector with same items
# itemnr <- as.numeric( substring( colnames(dat) ,2,2) )
# # fix mean at T2 to zero
# mu.fixed <- cbind( 2,0 )
# 
# #--- M1a: rasch.mml2 (in sirt)
# mod1a <- sirt::rasch.mml2(dat, Q=Q , est.b=itemnr , mu.fixed=mu.fixed)
# summary(mod1a)
# 
# #--- M1b: smirt (in sirt)
# mod1b <- sirt::smirt(dat, Qmatrix=Q , irtmodel="comp" , est.b= itemnr , 
#                   mu.fixed=mu.fixed )
# 
# #--- M1c: tam.mml (in TAM)
# 
# # assume equal item difficulty of I3T1 and I3T2, I4T1 and I4T2, ...
# # create draft design matrix and modify it
# A <- TAM::designMatrices(resp=dat)$A
# dimnames(A)[[1]] <- colnames(dat)
#   ##   > str(A)
#   ##    num [1:12, 1:2, 1:12] 0 0 0 0 0 0 0 0 0 0 ...
#   ##    - attr(*, "dimnames")=List of 3
#   ##     ..$ : chr [1:12] "Item01" "Item02" "Item03" "Item04" ...
#   ##     ..$ : chr [1:2] "Category0" "Category1"
#   ##     ..$ : chr [1:12] "I1T1" "I2T1" "I3T1" "I4T1" ...
# A1 <- A[  ,  , c(1:6 , 11:12 ) ]
# A1[7,2,3] <- -1     # difficulty(I3T1) = difficulty(I3T2)
# A1[8,2,4] <- -1     # I4T1 = I4T2
# A1[9,2,5] <- A1[10,2,6] <- -1
# dimnames(A1)[[3]] <- substring( dimnames(A1)[[3]],1,2)
#   ##   > A1[,2,]
#   ##        I1 I2 I3 I4 I5 I6 I7 I8
#   ##   I1T1 -1  0  0  0  0  0  0  0
#   ##   I2T1  0 -1  0  0  0  0  0  0
#   ##   I3T1  0  0 -1  0  0  0  0  0
#   ##   I4T1  0  0  0 -1  0  0  0  0
#   ##   I5T1  0  0  0  0 -1  0  0  0
#   ##   I6T1  0  0  0  0  0 -1  0  0
#   ##   I3T2  0  0 -1  0  0  0  0  0
#   ##   I4T2  0  0  0 -1  0  0  0  0
#   ##   I5T2  0  0  0  0 -1  0  0  0
#   ##   I6T2  0  0  0  0  0 -1  0  0
#   ##   I7T2  0  0  0  0  0  0 -1  0
#   ##   I8T2  0  0  0  0  0  0  0 -1
# 
# # estimate model
# # set intercept of second dimension (T2) to zero
# beta.fixed <- cbind( 1 , 2 , 0 )
# mod1c <- TAM::tam.mml( resp=dat , Q=Q , A=A1 , beta.fixed=beta.fixed)
# summary(mod1c)
# 
# #*************************************************
# # Model 2: 2-dimensional 2PL model
# #*************************************************
# 
# # set variance at T2 to 1
# variance.fixed <- cbind(2,2,1)
# 
# # M2a: rasch.mml2 (in sirt)
# mod2a <- sirt::rasch.mml2(dat, Q=Q , est.b=itemnr , est.a=itemnr , mu.fixed=mu.fixed,
#              variance.fixed=variance.fixed , mmliter=100)
# summary(mod2a)
# 
# #*************************************************
# # Model 3: Concurrent calibration by assuming invariant item parameters
# #*************************************************
# 
# library(mirt)   # use mirt for concurrent calibration
# data(data.long)
# dat <- data.long[,-1]
# I <- ncol(dat)
# 
# # create user defined function for between item dimensionality 4PL model
# name <- "4PLbw"
# par <- c("low"=0,"upp"=1,"a"=1,"d"=0 ,"dimItem"=1)
# est <- c(TRUE, TRUE,TRUE,TRUE,FALSE)
# # item response function
# irf <- function(par,Theta,ncat){    
#      low <- par[1]
#      upp <- par[2]
#      a <- par[3]
#      d <- par[4]
#      dimItem <- par[5]
#      P1 <- low + ( upp - low ) * plogis( a*Theta[,dimItem] + d )
#      cbind(1-P1, P1)
# }
# 
# # create item response function
# fourPLbetw <- mirt::createItem(name, par=par, est=est, P=irf)
# head(dat)
# 
# # create mirt model (use variable names in mirt.model)
# mirtsyn <- "
#      T1 = I1T1,I2T1,I3T1,I4T1,I5T1,I6T1
#      T2 = I3T2,I4T2,I5T2,I6T2,I7T2,I8T2
#      COV = T1*T2,,T2*T2
#      MEAN = T1
#      CONSTRAIN = (I3T1,I3T2,d),(I4T1,I4T2,d),(I5T1,I5T2,d),(I6T1,I6T2,d),
#                  (I3T1,I3T2,a),(I4T1,I4T2,a),(I5T1,I5T2,a),(I6T1,I6T2,a)     
#         "
# # create mirt model
# mirtmodel <- mirt::mirt.model( mirtsyn , itemnames=colnames(dat) )        
# # define parameters to be estimated
# mod3.pars <- mirt::mirt(dat, mirtmodel$model, rep( "4PLbw",I) , 
#                    customItems=list("4PLbw"=fourPLbetw), pars = "values")                
# # select dimensions
# ind <- intersect( grep("T2",mod3.pars$item) , which( mod3.pars$name == "dimItem" ) )
# mod3.pars[ind,"value"] <- 2
# # set item parameters low and upp to non-estimated
# ind <- which( mod3.pars$name %in% c("low","upp") ) 
# mod3.pars[ind,"est"] <- FALSE
# 
# # estimate 2PL model
# mod3 <- mirt::mirt(dat, mirtmodel$model, itemtype=rep( "4PLbw",I) , 
#                 customItems=list("4PLbw"=fourPLbetw), pars = mod3.pars , verbose=TRUE , 
#                 technical = list(NCYCLES=50)  )
# mirt.wrapper.coef(mod3)
# 
# #****** estimate model in lavaan
# library(lavaan)
# 
# # specify syntax
# lavmodel <- "
#              #**** T1
#              F1 =~ a1*I1T1+a2*I2T1+a3*I3T1+a4*I4T1+a5*I5T1+a6*I6T1
#              I1T1 | b1*t1 ; I2T1 | b2*t1 ; I3T1 | b3*t1 ; I4T1 | b4*t1
#              I5T1 | b5*t1 ; I6T1 | b6*t1
#              F1 ~~ 1*F1
#              #**** T2
#              F2 =~ a3*I3T2+a4*I4T2+a5*I5T2+a6*I6T2+a7*I7T2+a8*I8T2             
#              I3T2 | b3*t1 ; I4T2 | b4*t1 ; I5T2 | b5*t1 ; I6T2 | b6*t1
#              I7T2 | b7*t1 ; I8T2 | b8*t1 
#              F2 ~~ NA*F2
#              F2 ~ 1 
#              #*** covariance
#              F1 ~~ F2                          
#                 "                       
# # estimate model using theta parameterization                        
# mod3lav <- lavaan::cfa( data=dat , model=lavmodel,
#             std.lv = TRUE , ordered=colnames(dat) , parameterization="theta")
# summary(mod3lav , standardized=TRUE , fit.measures=TRUE , rsquare=TRUE)
# 
# #*************************************************
# # Model 4: Linking with items of different item slope groups
# #*************************************************
# 
# data(data.long)
# dat <- data.long
# # dataset for T1
# dat1 <- dat[ , grep( "T1" , colnames(dat) ) ]
# colnames(dat1) <- gsub("T1","" , colnames(dat1) )
# # dataset for T2
# dat2 <- dat[ , grep( "T2" , colnames(dat) ) ]
# colnames(dat2) <- gsub("T2","" , colnames(dat2) )
# 
# # 2PL model with slope groups T1
# mod1 <- rasch.mml2( dat1 , est.a = c( rep(1,2) , rep(2,4) ) ) 
# summary(mod1)
# 
# # 2PL model with slope groups T2
# mod2 <- rasch.mml2( dat2 , est.a = c( rep(1,4) , rep(2,2) ) ) 
# summary(mod2)
# 
# #------- Link 1: Haberman Linking
# # collect item parameters
# dfr1 <- data.frame( "study1" , mod1$item$item , mod1$item$a , mod1$item$b )
# dfr2 <- data.frame( "study2" , mod2$item$item , mod2$item$a , mod2$item$b )
# colnames(dfr2) <- colnames(dfr1) <- c("study" , "item" , "a" , "b" )
# itempars <- rbind( dfr1 , dfr2 )
# # Linking
# link1 <- linking.haberman(itempars=itempars)
# 
# #------- Link 2: Invariance alignment method
# # create objects for invariance.alignment
# nu <- rbind( c(mod1$item$thresh,NA,NA) , c(NA,NA,mod2$item$thresh) )
# lambda <- rbind( c(mod1$item$a,NA,NA) , c(NA,NA,mod2$item$a ) )
# colnames(lambda) <- colnames(nu) <- paste0("I",1:8)
# rownames(lambda) <- rownames(nu) <- c("T1" , "T2")
# # Linking
# link2a <- invariance.alignment( lambda , nu )
# summary(link2a)
# ## End(Not run)