karabatsos2004 {multinomineq}

Data: Item Responses Theory (Karabatsos & Sheu, 2004)

Description

The test was part of the 1992 Trial State Assessment in Reading at Grade 4, conducted by the National Assessments of Educational Progress (NAEP).

Usage

karabatsos2004

Format

A list with 4 matrices:

k.M:

Number of correct responses for participants with rest scores j=0,...,5 (i.e., the sum score minus the score for item i)

n.M:

Total number of participants for each cell of matrix k.M

k.IIO:

Number of correct responses for participants with sum scores j=0,...,6

n.IIO:

Total number of participants for each cell of matrix k.IIO

References

Karabatsos, G., & Sheu, C.-F. (2004). Order-constrained Bayes inference for dichotomous models of unidimensional nonparametric IRT. Applied Psychological Measurement, 28(2), 110-125. doi:10.1177/0146621603260678

See Also

The polytope for the nonparametric item response theory can be obtained using (see nirt_to_Ab).

Examples

data(karabatsos2004)
head(karabatsos2004)

######################################################
##### Testing Monotonicity (M)                   #####
##### (Karabatsos & Sheu, 2004, Table 3, p. 120) #####

IJ <- dim(karabatsos2004$k.M)
monotonicity <- nirt_to_Ab(IJ[1], IJ[2], axioms = "W1")
p <- sampling_binom(
  k = c(karabatsos2004$k.M),
  n = c(karabatsos2004$n.M),
  A = monotonicity$A, b = monotonicity$b,
  prior = c(.5, .5), M = 300
)

# posterior means (Table 4, p. 120)
post.mean <- matrix(apply(p, 2, mean), IJ[1],
  dimnames = dimnames(karabatsos2004$k.M)
)
round(post.mean, 2)

# posterior predictive checks (Table 4, p. 121)
ppp <- ppp_binom(p, c(karabatsos2004$k.M), c(karabatsos2004$n.M),
  by = 1:prod(IJ)
)
ppp <- matrix(ppp[, 3], IJ[1], dimnames = dimnames(karabatsos2004$k.M))
round(ppp, 2)


######################################################
##### Testing invariant item ordering (IIO)      #####
##### (Karabatsos & Sheu, 2004, Table 6, p. 122) #####

IJ <- dim(karabatsos2004$k.IIO)
iio <- nirt_to_Ab(IJ[1], IJ[2], axioms = "W2")
p <- sampling_binom(
  k = c(karabatsos2004$k.IIO),
  n = c(karabatsos2004$n.IIO),
  A = iio$A, b = iio$b,
  prior = c(.5, .5), M = 300
)
# posterior predictive checks (Table 6, p. 122)
ppp <- ppp_binom(prob = p, k = c(karabatsos2004$k.IIO),
                 n = c(karabatsos2004$n.IIO), by = 1:prod(IJ))
matrix(ppp[,3], 7, dimnames = dimnames(karabatsos2004$k.IIO))

# for each item:
ppp <- ppp_binom(p, c(karabatsos2004$k.IIO), c(karabatsos2004$n.IIO),
                 by = rep(1:IJ[2], each = IJ[1]))
round(ppp[,3], 2)