probs.GGUM | R Documentation |
probs.GGUM
computes model probabilities for the GGUM (and
the GUM) for given item and person parameters.
probs.GGUM(alpha, delta, taus, theta, C)
alpha |
A vector of length I with the discrimination parameters. |
delta |
A vector of length I with the difficulty parameters. |
taus |
An IxM matrix with the threshold parameters (M = 2*max(C)+1). |
theta |
A vector of length N with the person parameters. |
C |
C is the number of observable response categories minus 1 (i.e., the item scores will be in the set \{0, 1, ..., C\}). It should either be a vector of I elements or a scalar. In the latter case, it is assumed that C applies to all items. |
The function returns an NxIxK array with the
GGUM probabilities, with K=max(C)+1. To retrieve the
GUM-based probabilities just constrain alpha to a unit vector of length I
(i.e., alpha = rep(1, I)
). In this case, make sure C
is
constant across items.
This function computes the GGUM-based probabilities for all
(person, item, response category) combinations. For the GGUM formula see
the help for function GGUM
(GGUM
).
Jorge N. Tendeiro, tendeiro@hiroshima-u.ac.jp
C <- c(3, 3, 3, 5, 5) gen <- GenData.GGUM(10, 5, C, seed = 456) gen.alpha <- gen$alpha.gen gen.delta <- gen$delta.gen gen.taus <- gen$taus.gen gen.theta <- gen$theta.gen # Compute model probabilities for the parameters above: Ps <- probs.GGUM(gen.alpha, gen.delta, gen.taus, gen.theta, C) Ps # In particular, the sum of the probabilities across all response options # (i.e., the third dimension) should be 1 for all (person, item) combinations: apply(Ps, 1:2, sum)
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