data.long: Longitudinal Dataset

Description Usage Format Examples

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

1

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

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
## 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 <- sirt::rasch.mml2( dat1, est.a=c( rep(1,2), rep(2,4) ) )
summary(mod1)

# 2PL model with slope groups T2
mod2 <- sirt::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 <- sirt::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 <- sirt::invariance.alignment( lambda, nu )
summary(link2a)

## End(Not run)

alexanderrobitzsch/sirt documentation built on June 27, 2021, 12:03 a.m.