karabatsos2004 | R Documentation |
The test was part of the 1992 Trial State Assessment in Reading at Grade 4, conducted by the National Assessments of Educational Progress (NAEP).
karabatsos2004
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
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
The polytope for the nonparametric item response theory can be obtained
using (see nirt_to_Ab
).
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)
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