Description Usage Arguments Value Details Author(s) References Examples
GUM
estimates all item parameters for the GUM.
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data 
The NxI data matrix. The item scores are coded 0, 1, ..., C for an item with (C+1) observable response categories. 
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 be a scalar since the GUM expects all items to be based on the same number of observable response categories. 
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 C. 
alpha 
In case of the GUM this is simply a vector of 1s. 
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 graded unfolding model (GUM; Roberts & Laughlin, 1996)
is a constrained version of the GGUM (Roberts et al., 2000; see
GGUM
). GUM is constrained in two ways: All
discrimination parameters are fixed to unity and the threshold parameters
are shared across items. In particular, the last constraint implies that
only data with the same response categories across items should be used
(i.e., C is constant for all items).
Estimated GUM parameters are used as the second step of fitting the more general GGUM. Since under the GGUM data may include items with different number of response categories, the code to fitting the GUM was internally extended to accommodate for this.
The marginal maximum likelihood algorithm of Roberts et al. (2000) was implemented.
Jorge N. Tendeiro, tendeiro@hiroshimau.ac.jp
RobertsLaughlin1996GGUM
\insertRefRobertsetal2000GGUM
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