GGUM | R Documentation |
GGUM
estimates all item parameters for the GGUM.
GGUM(
data,
C,
SE = TRUE,
precision = 4,
N.nodes = 30,
max.outer = 60,
max.inner = 60,
tol = 0.001
)
data |
The |
C |
|
SE |
Logical value: Estimate the standard errors of the item parameter
estimates? Default is |
precision |
Number of decimal places of the results (default = 4). |
N.nodes |
Number of nodes for numerical integration (default = 30). |
max.outer |
Maximum number of outer iterations (default = 60). |
max.inner |
Maximum number of inner iterations (default = 60). |
tol |
Convergence tolerance (default = .001). |
The function returns a list (an object of class GGUM
) with 12
elements:
data |
Data matrix. |
C |
Vector |
alpha |
The estimated discrimination parameters for the GGUM. |
delta |
The estimated difficulty parameters. |
taus |
The estimated threshold parameters. |
SE |
The standard errors of the item parameters estimates. |
rows.rm |
Indices of rows removed from the data before fitting the model, due to complete disagreement. |
N.nodes |
Number of nodes for numerical integration. |
tol.conv |
Loss function value at convergence (it is smaller than
|
iter.inner |
Number of inner iterations (it is equal to 1 upon convergence). |
model |
Model fitted. |
InformationCrit |
Loglikelihood, number of model parameters, AIC, BIC, CAIC. |
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
.
The marginal maximum likelihood algorithm of Roberts et al. (2000) was implemented.
Jorge N. Tendeiro, tendeiro@hiroshima-u.ac.jp
RobertsLaughlin1996GGUM
\insertRefRobertsetal2000GGUM
## Not run:
# Example 1 - Same value C across items:
# Generate data:
gen1 <- GenData.GGUM(2000, 10, 2, seed = 125)
# Fit the GGUM:
fit1 <- GGUM(gen1$data, 2)
# Compare true and estimated item parameters:
cbind(gen1$alpha, fit1$alpha)
cbind(gen1$delta, fit1$delta)
cbind(c(gen1$taus[, 4:5]), c(fit1$taus[, 4:5]))
# Example 2 - Different C across items:
# Generate data:
set.seed(1); C <- sample(3:5, 10, replace = TRUE)
gen2 <- GenData.GGUM(2000, 10, C, seed = 125)
# Fit the GGUM:
fit2 <- GGUM(gen2$data, C)
# Compare true and estimated item parameters:
cbind(gen2$alpha, fit2$alpha)
cbind(gen2$delta, fit2$delta)
cbind(c(gen2$taus[, 7:11]), c(fit2$taus[, 7:11]))
## End(Not run)
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