#############################################################################
# EXAMPLE 1: Dimitrov (2003) Table 1 - 2PL model
#############################################################################
# item discriminations
a <- 1.7*c(0.449,0.402,0.232,0.240,0.610,0.551,0.371,0.321,0.403,0.434,0.459,
0.410,0.302,0.343,0.225,0.215,0.487,0.608,0.341,0.465)
# item difficulties
b <- c( -2.554,-2.161,-1.551,-1.226,-0.127,-0.855,-0.568,-0.277,-0.017,
0.294,0.532,0.773,1.004,1.250,1.562,1.385,2.312,2.650,2.712,3.000 )
marginal.truescore.reliability( b=b, a=a )
## Reliability=0.606
#############################################################################
# EXAMPLE 2: Dimitrov (2003) Table 2
# 3PL model: Poetry items (4 items)
#############################################################################
# slopes, difficulties and guessing parameters
a <- 1.7*c(1.169,0.724,0.554,0.706 )
b <- c(0.468,-1.541,-0.042,0.698 )
c <- c(0.159,0.211,0.197,0.177 )
res <- sirt::marginal.truescore.reliability( b=b, a=a, c=c)
## Reliability=0.403
## > round( res$item, 3 )
## item pi sig2.tau sig2.error rel.item
## 1 1 0.463 0.063 0.186 0.252
## 2 2 0.855 0.017 0.107 0.135
## 3 3 0.605 0.026 0.213 0.107
## 4 4 0.459 0.032 0.216 0.130
#############################################################################
# EXAMPLE 3: Reading Data
#############################################################################
data( data.read)
#***
# Model 1: 1PL
mod <- sirt::rasch.mml2( data.read )
marginal.truescore.reliability( b=mod$item$b )
## Reliability=0.653
#***
# Model 2: 2PL
mod <- sirt::rasch.mml2( data.read, est.a=1:12 )
marginal.truescore.reliability( b=mod$item$b, a=mod$item$a)
## Reliability=0.696
if (FALSE) {
# compare results with Cronbach's alpha and McDonald's omega
# posing a 'wrong model' for normally distributed data
library(psych)
psych::omega(dat, nfactors=1) # 1 factor
## Omega_h for 1 factor is not meaningful, just omega_t
## Omega
## Call: omega(m=dat, nfactors=1)
## Alpha: 0.69
## G.6: 0.7
## Omega Hierarchical: 0.66
## Omega H asymptotic: 0.95
## Omega Total 0.69
##! Note that alpha in psych is the standardized one.
}
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