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 |
|
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|\theta_n) =
\frac{f(z) + f(M-z)}{\sum_{w=0}^C\left[f(w)+f(M-w)\right]},
f(w) = exp\left\{\alpha_i\left[w(\theta_n-\delta_i)-
\sum_{k=0}^w\tau_{ik}\right]\right\},
where:
The subscripts i
and n
identify the item
and person, respectively.
z=0,\ldots,C
denotes
the observed answer response.
M = 2C + 1
is the number of
subjective response options minus 1.
\theta_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,\ldots,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\not= 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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