sirt (version 1.14-0)

data.reck: Datasets from Reckase' Book Multidimensional Item Response Theory

Description

Some simulated datasets from Reckase (2009).

Usage

data(data.reck21)
data(data.reck61DAT1)
data(data.reck61DAT2)
data(data.reck73C1a)
data(data.reck73C1b)
data(data.reck75C2)
data(data.reck78ExA)
data(data.reck79ExB)

Format

• The format of the data.reck21 (Table 2.1, p. 45) is: List of 2 $ data: num [1:2500, 1:50] 0 0 0 1 1 0 0 0 1 0 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:50] "I0001" "I0002" "I0003" "I0004" ... $ pars:'data.frame': ..$ a: num [1:50] 1.83 1.38 1.47 1.53 0.88 0.82 1.02 1.19 1.15 0.18 ... ..$ b: num [1:50] 0.91 0.81 0.06 -0.8 0.24 0.99 1.23 -0.47 2.78 -3.85 ... ..$ c: num [1:50] 0 0 0 0.25 0.21 0.29 0.26 0.19 0 0.21 ...
• The format of the datasets data.reck61DAT1 and data.reck61DAT2 (Table 6.1, p. 153) is List of 4 $ data : num [1:2500, 1:30] 1 0 0 1 1 0 0 1 1 0 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:30] "A01" "A02" "A03" "A04" ... $ pars :'data.frame': ..$ a1: num [1:30] 0.747 0.46 0.861 1.014 0.552 ... ..$ a2: num [1:30] 0.025 0.0097 0.0067 0.008 0.0204 0.0064 0.0861 ... ..$ a3: num [1:30] 0.1428 0.0692 0.404 0.047 0.1482 ... ..$ d : num [1:30] 0.183 -0.192 -0.466 -0.434 -0.443 ... $ mu : num [1:3] -0.4 -0.7 0.1 $ sigma: num [1:3, 1:3] 1.21 0.297 1.232 0.297 0.81 ... The dataset data.reck61DAT2 has correlated dimensions while data.reck61DAT1 has uncorrelated dimensions.
• Datasets data.reck73C1a and data.reck73C1b use item parameters from Table 7.3 (p. 188). The dataset C1a has uncorrelated dimensions, while C1b has perfectly correlated dimensions. The items are sensitive to 3 dimensions. The format of the datasets is List of 4 $ data : num [1:2500, 1:30] 1 0 1 1 1 0 1 1 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:30] "A01" "A02" "A03" "A04" ... $ pars :'data.frame': 30 obs. of 4 variables: ..$ a1: num [1:30] 0.747 0.46 0.861 1.014 0.552 ... ..$ a2: num [1:30] 0.025 0.0097 0.0067 0.008 0.0204 0.0064 ... ..$ a3: num [1:30] 0.1428 0.0692 0.404 0.047 0.1482 ... ..$ d : num [1:30] 0.183 -0.192 -0.466 -0.434 -0.443 ... $ mu : num [1:3] 0 0 0 $ sigma: num [1:3, 1:3] 0.167 0.236 0.289 0.236 0.334 ...
• The dataset data.reck75C2 is simulated using item parameters from Table 7.5 (p. 191). It contains items which are sensitive to only one dimension but individuals which have abilities in three uncorrelated dimensions. The format is List of 4 $ data : num [1:2500, 1:30] 0 0 1 1 1 0 0 1 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:30] "A01" "A02" "A03" "A04" ... $ pars :'data.frame': 30 obs. of 4 variables: ..$ a1: num [1:30] 0.56 0.48 0.67 0.57 0.54 0.74 0.7 0.59 0.63 0.64 ... ..$ a2: num [1:30] 0.62 0.53 0.63 0.69 0.58 0.69 0.75 0.63 0.64 0.64 ... ..$ a3: num [1:30] 0.46 0.42 0.43 0.51 0.41 0.48 0.46 0.5 0.51 0.46 ... ..$ d : num [1:30] 0.1 0.06 -0.38 0.46 0.14 0.31 0.06 -1.23 0.47 1.06 ... $ mu : num [1:3] 0 0 0 $ sigma: num [1:3, 1:3] 1 0 0 0 1 0 0 0 1
• The dataset data.reck78ExA contains simulated item responses from Table 7.8 (p. 204 ff.). There are three item clusters and two ability dimensions. The format is List of 4 $ data : num [1:2500, 1:50] 0 1 1 0 1 0 0 0 0 0 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:50] "A01" "A02" "A03" "A04" ... $ pars :'data.frame': 50 obs. of 3 variables: ..$ a1: num [1:50] 0.889 1.057 1.047 1.178 1.029 ... ..$ a2: num [1:50] 0.1399 0.0432 0.016 0.0231 0.2347 ... ..$ d : num [1:50] 0.2724 1.2335 -0.0918 -0.2372 0.8471 ... $ mu : num [1:2] 0 0 $ sigma: num [1:2, 1:2] 1 0 0 1
• The dataset data.reck79ExB contains simulated item responses from Table 7.9 (p. 207 ff.). There are three item clusters and three ability dimensions. The format is List of 4 $ data : num [1:2500, 1:50] 1 1 0 1 0 0 0 1 1 0 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:50] "A01" "A02" "A03" "A04" ... $ pars :'data.frame': 50 obs. of 4 variables: ..$ a1: num [1:50] 0.895 1.032 1.036 1.163 1.022 ... ..$ a2: num [1:50] 0.052 0.132 0.144 0.13 0.165 ... ..$ a3: num [1:50] 0.0722 0.1923 0.0482 0.1321 0.204 ... ..$ d : num [1:50] 0.2724 1.2335 -0.0918 -0.2372 0.8471 ... $ mu : num [1:3] 0 0 0 $ sigma: num [1:3, 1:3] 1 0 0 0 1 0 0 0 1

Source

Simulated datasets

References

Reckase, M. (2009). Multidimensional item response theory. New York: Springer.

Examples

## Not run: 	
# #############################################################################
# # EXAMPLE 1: data.reck21 dataset, Table 2.1, p. 45	
# #############################################################################
# data(data.reck21)
# 
# dat <- data.reck21$dat      # extract dataset
# 
# # items with zero guessing parameters
# guess0 <- c( 1 , 2 , 3 , 9 ,11 ,27 ,30 ,35 ,45 ,49 ,50 )
# I <- ncol(dat)
# 
# #***
# # Model 1: 3PL estimation using rasch.mml2
# est.c <- est.a <- 1:I
# est.c[ guess0 ] <- 0
# mod1 <- sirt::rasch.mml2( dat , est.a=est.a , est.c=est.c , mmliter= 300 )
# summary(mod1)
# 
# #***
# # Model 2: 3PL estimation using smirt
# Q <- matrix(1,I,1)
# mod2 <- sirt::smirt( dat , Qmatrix=Q , est.a= "2PL"  , est.c=est.c , increment.factor=1.01)
# summary(mod2)
# 
# #***
# # Model 3: estimation in mirt package
# library(mirt)
# itemtype <- rep("3PL" , I )
# itemtype[ guess0 ] <- "2PL"
# mod3 <- mirt::mirt(dat, 1, itemtype = itemtype , verbose=TRUE)
# summary(mod3)
# 
# c3 <- unlist( coef(mod3) )[ 1:(4*I) ]
# c3 <- matrix( c3 , I , 4 , byrow=TRUE )
# # compare estimates of rasch.mml2, smirt and true parameters
# round( cbind( mod1$item$c , mod2$item$c ,c3[,3]  ,data.reck21$pars$c ) , 2 )
# round( cbind( mod1$item$a , mod2$item$a.Dim1 ,c3[,1], data.reck21$pars$a ) , 2 )
# round( cbind( mod1$item$b , mod2$item$b.Dim1 / mod2$item$a.Dim1 , - c3[,2] / c3[,1] , 
#             data.reck21$pars$b ) , 2 )
#             
# #############################################################################
# # EXAMPLE 2: data.reck61 dataset, Table 6.1, p. 153	
# #############################################################################            
# 
# data(data.reck61DAT1)
# dat <- data.reck61DAT1$data
# 
# #***
# # Model 1: Exploratory factor analysis
# 
# #-- Model 1a: tam.fa in TAM
# library(TAM)
# mod1a <- TAM::tam.fa( dat , irtmodel="efa" , nfactors=3 )
# # varimax rotation
# varimax(mod1a$B.stand)
# 
# # Model 1b: EFA in NOHARM (Promax rotation)
# mod1b <- sirt::R2noharm( dat = dat , model.type="EFA" ,  dimensions = 3 , 
#               writename = "reck61__3dim_efa", noharm.path = "c:/NOHARM" ,dec = ",")
# summary(mod1b)
# 
# # Model 1c: EFA with noharm.sirt
# mod1c <- sirt::noharm.sirt( dat=dat , dimensions=3  )
# summary(mod1c)
# plot(mod1c)
# 
# # Model 1d: EFA with 2 dimensions in noharm.sirt
# mod1d <- sirt::noharm.sirt( dat=dat , dimensions=2  )
# summary(mod1d)
# plot(mod1d , efa.load.min=.2)   # plot loadings of at least .20
# 
# #***
# # Model 2: Confirmatory factor analysis
# 
# #-- Model 2a: tam.fa in TAM
# dims <- c( rep(1,10) , rep(3,10) , rep(2,10)  )
# Qmatrix <- matrix( 0 , nrow=30 , ncol=3 )
# Qmatrix[ cbind( 1:30 , dims) ] <- 1
# mod2a <- TAM::tam.mml.2pl( dat ,Q=Qmatrix , 
#             control=list( snodes=1000, QMC=TRUE , maxiter=200) )
# summary(mod2a)
# 
# #-- Model 2b: smirt in sirt
# mod2b <- sirt::smirt( dat ,Qmatrix =Qmatrix , est.a="2PL" , maxiter=20 , qmcnodes=1000 )
# summary(mod2b)
# 
# #-- Model 2c: rasch.mml2 in sirt
# mod2c <- sirt::rasch.mml2( dat ,Qmatrix =Qmatrix , est.a= 1:30 , 
#                 mmliter =200 , theta.k = seq(-5,5,len=11) )
# summary(mod2c)
# 
# #-- Model 2d: mirt in mirt
# cmodel <- mirt::mirt.model("
#      F1 = 1-10
#      F2 = 21-30
#      F3 = 11-20
#      COV = F1*F2, F1*F3 , F2*F3 " )
# mod2d <- mirt::mirt(dat, cmodel , verbose=TRUE)
# summary(mod2d)
# coef(mod2d)
# 
# #-- Model 2e: CFA in NOHARM
# # specify covariance pattern
# P.pattern <- matrix( 1 , ncol=3 , nrow=3 )
# P.init <- .4*P.pattern
# diag(P.pattern) <- 0
# diag(P.init) <- 1
# # fix all entries in the loading matrix to 1
# F.pattern <- matrix( 0 , nrow=30 , ncol=3 )
# F.pattern[1:10,1] <- 1
# F.pattern[21:30,2] <- 1
# F.pattern[11:20,3] <- 1
# F.init <- F.pattern
# # estimate model
# mod2e <- sirt::R2noharm( dat = dat , model.type="CFA" , P.pattern=P.pattern, 
#             P.init=P.init , F.pattern=F.pattern, F.init=F.init ,
#             writename = "reck61__3dim_cfa", noharm.path = "c:/NOHARM" ,dec = ",")
# summary(mod2e)
# 
# #-- Model 2f: CFA with noharm.sirt
# mod2f <- sirt::noharm.sirt( dat = dat , Fval=F.init , Fpatt = F.pattern ,
#                  Pval=P.init , Ppatt = P.pattern )                      
# summary(mod2f)
# 
# #############################################################################
# # EXAMPLE 3: DETECT analysis data.reck78ExA and data.reck79ExB
# ############################################################################# 
# 
# data(data.reck78ExA)
# data(data.reck79ExB)
# 
# #************************
# # Example A
# dat <- data.reck78ExA$data
# #- estimate person score
# score <- stats::qnorm( ( rowMeans( dat )+.5 )  / ( ncol(dat) + 1 ) )
# #- extract item cluster
# itemcluster <- substring( colnames(dat) , 1 , 1 )
# #- confirmatory DETECT Item cluster
# detectA <- sirt::conf.detect( data = dat , score = score , itemcluster = itemcluster )
#   ##          unweighted weighted
#   ##   DETECT      0.571    0.571
#   ##   ASSI        0.523    0.523
#   ##   RATIO       0.757    0.757
# 
# #- exploratory DETECT analysis
# detect_explA <- sirt::expl.detect(data=dat, score, nclusters=10, N.est = nrow(dat)/2  )
#   ##  Optimal Cluster Size is  5  (Maximum of DETECT Index)
#   ##     N.Cluster N.items N.est N.val         size.cluster DETECT.est ASSI.est
#   ##   1         2      50  1250  1250                31-19      0.531    0.404
#   ##   2         3      50  1250  1250             10-19-21      0.554    0.407
#   ##   3         4      50  1250  1250           10-19-14-7      0.630    0.509
#   ##   4         5      50  1250  1250         10-19-3-7-11      0.653    0.546
#   ##   5         6      50  1250  1250       10-12-7-3-7-11      0.593    0.458
#   ##   6         7      50  1250  1250      10-12-7-3-7-9-2      0.604    0.474
#   ##   7         8      50  1250  1250    10-12-7-3-3-9-4-2      0.608    0.481
#   ##   8         9      50  1250  1250  10-12-7-3-3-5-4-2-4      0.617    0.494
#   ##   9        10      50  1250  1250 10-5-7-7-3-3-5-4-2-4      0.592    0.460
# 
# # cluster membership
# cluster_membership <- detect_explA$itemcluster$cluster3
# # Cluster 1:
# colnames(dat)[ cluster_membership == 1 ]
#   ##   [1] "A01" "A02" "A03" "A04" "A05" "A06" "A07" "A08" "A09" "A10"
# # Cluster 2:
# colnames(dat)[ cluster_membership == 2 ]
#   ##    [1] "B11" "B12" "B13" "B14" "B15" "B16" "B17" "B18" "B19" "B20" "B21" "B22"
#   ##   [13] "B23" "B25" "B26" "B27" "B28" "B29" "B30"
# # Cluster 3:
# colnames(dat)[ cluster_membership == 3 ]
#   ##    [1] "B24" "C31" "C32" "C33" "C34" "C35" "C36" "C37" "C38" "C39" "C40" "C41"
#   ##   [13] "C42" "C43" "C44" "C45" "C46" "C47" "C48" "C49" "C50"
# 
# #************************
# # Example B
# dat <- data.reck79ExB$data
# #- estimate person score
# score <- stats::qnorm( ( rowMeans( dat )+.5 )  / ( ncol(dat) + 1 ) )
# #- extract item cluster
# itemcluster <- substring( colnames(dat) , 1 , 1 )
# #- confirmatory DETECT Item cluster
# detectB <- sirt::conf.detect( data = dat , score = score , itemcluster = itemcluster )
#   ##          unweighted weighted
#   ##   DETECT      0.715    0.715
#   ##   ASSI        0.624    0.624
#   ##   RATIO       0.855    0.855
# 
# #- exploratory DETECT analysis
# detect_explB <- sirt::expl.detect(data=dat, score, nclusters=10, N.est = nrow(dat)/2  )
#   ##   Optimal Cluster Size is  4  (Maximum of DETECT Index)
#   ##   
#   ##     N.Cluster N.items N.est N.val         size.cluster DETECT.est ASSI.est
#   ##   1         2      50  1250  1250                30-20      0.665    0.546
#   ##   2         3      50  1250  1250             10-20-20      0.686    0.585
#   ##   3         4      50  1250  1250           10-20-8-12      0.728    0.644
#   ##   4         5      50  1250  1250         10-6-14-8-12      0.654    0.553
#   ##   5         6      50  1250  1250       10-6-14-3-12-5      0.659    0.561
#   ##   6         7      50  1250  1250      10-6-14-3-7-5-5      0.664    0.576
#   ##   7         8      50  1250  1250     10-6-7-7-3-7-5-5      0.616    0.518
#   ##   8         9      50  1250  1250   10-6-7-7-3-5-5-5-2      0.612    0.512
#   ##   9        10      50  1250  1250 10-6-7-7-3-5-3-5-2-2      0.613    0.512
# ## End(Not run)