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 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 either be a vector of I elements or a scalar. In the latter case, it is assumed that C applies to all items. |
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 |
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|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.
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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