Some Datasets from McDonald's Test Theory Book
data.mcdonald.RdSome datasets from McDonald (1999), especially related to using NOHARM for item response modeling. See Examples below.
Format
The format of the ACT15 data
data.mcdonald.act15is:num [1:15, 1:15] 0.49 0.44 0.38 0.3 0.29 0.13 0.23 0.16 0.16 0.23 ...- attr(*, "dimnames")=List of 2..$ : chr [1:15] "A01" "A02" "A03" "A04" .....$ : chr [1:15] "A01" "A02" "A03" "A04" ...The dataset (which is the product-moment covariance matrix) is obtained from Ch. 12 in McDonald (1999).
The format of the LSAT6 data
data.mcdonald.LSAT6is:'data.frame': 1004 obs. of 5 variables:$ L1: int 0 0 0 0 0 0 0 0 0 0 ...$ L2: int 0 0 0 0 0 0 0 0 0 0 ...$ L3: int 0 0 0 0 0 0 0 0 0 0 ...$ L4: int 0 0 0 0 0 0 0 0 0 1 ...$ L5: int 0 0 0 1 1 1 1 1 1 0 ...The dataset is obtained from Ch. 6 in McDonald (1999).
The format of the rape myth scale data
data.mcdonald.rapeisList of 2$ lambda: num [1:2, 1:19] 1.13 0.88 0.85 0.77 0.79 0.55 1.12 1.01 0.99 0.79 .....- attr(*, "dimnames")=List of 2.. ..$ : chr [1:2] "male" "female".. ..$ : chr [1:19] "I1" "I2" "I3" "I4" ...$ nu : num [1:2, 1:19] 2.88 1.87 3.12 2.32 2.13 1.43 3.79 2.6 3.01 2.11 .....- attr(*, "dimnames")=List of 2.. ..$ : chr [1:2] "male" "female".. ..$ : chr [1:19] "I1" "I2" "I3" "I4" ...The dataset is obtained from Ch. 15 in McDonald (1999).
Examples
if (FALSE) {
#############################################################################
# EXAMPLE 1: LSAT6 data | Chapter 12 McDonald (1999)
#############################################################################
data(data.mcdonald.act15)
#************
# Model 1: 2-parameter normal ogive model
#++ NOHARM estimation
I <- ncol(dat)
# covariance structure
P.pattern <- matrix( 0, ncol=1, nrow=1 )
P.init <- 1+0*P.pattern
# fix all entries in the loading matrix to 1
F.pattern <- matrix( 1, nrow=I, ncol=1 )
F.init <- F.pattern
# estimate model
mod1a <- sirt::R2noharm( dat=dat, model.type="CFA", F.pattern=F.pattern,
F.init=F.init, P.pattern=P.pattern, P.init=P.init,
writename="LSAT6__1dim_2pno", noharm.path=noharm.path, dec="," )
summary(mod1a, logfile="LSAT6__1dim_2pno__SUMMARY")
#++ pairwise marginal maximum likelihood estimation using the probit link
mod1b <- sirt::rasch.pml3( dat, est.a=1:I, est.sigma=FALSE)
#************
# Model 2: 1-parameter normal ogive model
#++ NOHARM estimation
# covariance structure
P.pattern <- matrix( 0, ncol=1, nrow=1 )
P.init <- 1+0*P.pattern
# fix all entries in the loading matrix to 1
F.pattern <- matrix( 2, nrow=I, ncol=1 )
F.init <- 1+0*F.pattern
# estimate model
mod2a <- sirt::R2noharm( dat=dat, model.type="CFA", F.pattern=F.pattern,
F.init=F.init, P.pattern=P.pattern, P.init=P.init,
writename="LSAT6__1dim_1pno", noharm.path=noharm.path, dec="," )
summary(mod2a, logfile="LSAT6__1dim_1pno__SUMMARY")
# PMML estimation
mod2b <- sirt::rasch.pml3( dat, est.a=rep(1,I), est.sigma=FALSE )
summary(mod2b)
#************
# Model 3: 3-parameter normal ogive model with fixed guessing parameters
#++ NOHARM estimation
# covariance structure
P.pattern <- matrix( 0, ncol=1, nrow=1 )
P.init <- 1+0*P.pattern
# fix all entries in the loading matrix to 1
F.pattern <- matrix( 1, nrow=I, ncol=1 )
F.init <- 1+0*F.pattern
# estimate model
mod <- sirt::R2noharm( dat=dat, model.type="CFA", guesses=rep(.2,I),
F.pattern=F.pattern, F.init=F.init, P.pattern=P.pattern,
P.init=P.init, writename="LSAT6__1dim_3pno",
noharm.path=noharm.path, dec="," )
summary(mod, logfile="LSAT6__1dim_3pno__SUMMARY")
#++ logistic link function employed in smirt function
mod1d <- sirt::smirt(dat, Qmatrix=F.pattern, est.a=matrix(1:I,I,1), c.init=rep(.2,I))
summary(mod1d)
#############################################################################
# EXAMPLE 2: ACT15 data | Chapter 6 McDonald (1999)
#############################################################################
data(data.mcdonald.act15)
pm <- data.mcdonald.act15
#************
# Model 1: 2-dimensional exploratory factor analysis
mod1 <- sirt::R2noharm( pm=pm, n=1000, model.type="EFA", dimensions=2,
writename="ACT15__efa_2dim", noharm.path=noharm.path, dec="," )
summary(mod1)
#************
# Model 2: 2-dimensional independent clusters basis solution
P.pattern <- matrix(1,2,2)
diag(P.pattern) <- 0
P.init <- 1+0*P.pattern
F.pattern <- matrix(0,15,2)
F.pattern[ c(1:5,11:15),1] <- 1
F.pattern[ c(6:10,11:15),2] <- 1
F.init <- F.pattern
# estimate model
mod2 <- sirt::R2noharm( pm=pm, n=1000, model.type="CFA", F.pattern=F.pattern,
F.init=F.init, P.pattern=P.pattern,P.init=P.init,
writename="ACT15_indep_clusters", noharm.path=noharm.path, dec="," )
summary(mod2)
#************
# Model 3: Hierarchical model
P.pattern <- matrix(0,3,3)
P.init <- P.pattern
diag(P.init) <- 1
F.pattern <- matrix(0,15,3)
F.pattern[,1] <- 1 # all items load on g factor
F.pattern[ c(1:5,11:15),2] <- 1 # Items 1-5 and 11-15 load on first nested factor
F.pattern[ c(6:10,11:15),3] <- 1 # Items 6-10 and 11-15 load on second nested factor
F.init <- F.pattern
# estimate model
mod3 <- sirt::R2noharm( pm=pm, n=1000, model.type="CFA", F.pattern=F.pattern,
F.init=F.init, P.pattern=P.pattern, P.init=P.init,
writename="ACT15_hierarch_model", noharm.path=noharm.path, dec="," )
summary(mod3)
#############################################################################
# EXAMPLE 3: Rape myth scale | Chapter 15 McDonald (1999)
#############################################################################
data(data.mcdonald.rape)
lambda <- data.mcdonald.rape$lambda
nu <- data.mcdonald.rape$nu
# obtain multiplier for factor loadings (Formula 15.5)
k <- sum( lambda[1,] * lambda[2,] ) / sum( lambda[2,]^2 )
## [1] 1.263243
# additive parameter (Formula 15.7)
c <- sum( lambda[2,]*(nu[1,]-nu[2,]) ) / sum( lambda[2,]^2 )
## [1] 1.247697
# SD in the female group
1/k
## [1] 0.7916132
# M in the female group
- c/k
## [1] -0.9876932
# Burt's coefficient of factorial congruence (Formula 15.10a)
sum( lambda[1,] * lambda[2,] ) / sqrt( sum( lambda[1,]^2 ) * sum( lambda[2,]^2 ) )
## [1] 0.9727831
# congruence for mean parameters
sum( (nu[1,]-nu[2,]) * lambda[2,] ) / sqrt( sum( (nu[1,]-nu[2,])^2 ) * sum( lambda[2,]^2 ) )
## [1] 0.968176
}