GenData.GGUM | R Documentation |
GenData.GGUM
generates all model parameters (items and
persons) and item scores.
GenData.GGUM(N, I, C, model = "GGUM", seed = 123)
N |
Number of persons (rows). |
I |
Number of items (columns). |
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. |
model |
A string identifying the model. Possible values are "GUM" or "GGUM" (default). |
seed |
An integer, allowing the user to control the generation process (for replication purposes). |
The function returns a list with five elements:
alpha.gen |
The discrimination parameters. |
delta.gen |
The difficulty parameters. |
taus.gen |
The threshold parameters. |
theta.gen |
The person parameters. |
data |
The (NxI) data matrix. The item scores are coded 0, 1, ..., C for an item with (C+1) observable response categories. |
The generalized graded unfolding model (GGUM; Roberts & Laughlin, 1996; Roberts et al., 2000) is given by
P(Z_i = z|t_n) = ( f(z) + f(M-z) ) / (sum( f(w) + f(M - w); w = 0, ..., C )),
f(w) = exp( alpha_i ( w(t_n - delta_i) - sum( tau_ik; k = 0, ..., w) ) ),
where:
The subscripts i and n identify the item and person, respectively.
z = 0, ..., C denotes the observed answer response.
M = 2C + 1 is the number of subjective response options minus 1.
t_n is the latent trait score for person n.
alpha_i is the item slope (discrimination).
delta_i is the item location.
tau_ik (k = 1, ..., M ) are the threshold parameters.
Parameter tau_i0 is arbitrarily constrained to zero and the threshold parameters are constrained to symmetry around zero, that is, tau_{i(C+1)} = 0 and tau_{iz} = -tau_{i(M-z+1)} for z != 0.
Parameters alpha_i are randomly uniformly drawn from the (.5, 2) interval. Parameters delta_i are randomly drawn from the standard normal distribution bounded between -2 and 2. The threshold parameters are generated following the same procedure of Roberts, Donoghue, and Laughlin (2002). Finally, the person parameters are randomly drawn from the standard normal distribution.
If model = "GUM"
the data based on the GUM (Roberts and Laughlin,
1996) model are generated. The GUM is a constrained version of the GGUM,
where all discrimination parameters are equal to 1 and the item thresholds
are shared by all items.
Jorge N. Tendeiro, tendeiro@hiroshima-u.ac.jp
gen1 <- GenData.GGUM(500, 10, 5, seed = 456) gen1$data # Retrieve the data. gen1$alpha.gen # The discrimination parameters. # Generate data based on items varying in the number of observable response categories: gen2 <- GenData.GGUM(500, 5, c(5, 5, 5, 4, 4), seed = 789)
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