GUM: Fit the graded unfolding model (GUM)

In GGUM: Generalized Graded Unfolding Model

Fit the graded unfolding model (GUM)

Description

GUM estimates all item parameters for the GUM.

Usage

GUM(
  data,
  C,
  SE = TRUE,
  precision = 4,
  N.nodes = 30,
  max.outer = 60,
  max.inner = 60,
  tol = 0.001
)

Arguments

data	The N\times I data matrix. The item scores are coded 0, 1, \ldots, 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 TRUE.
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).

Value

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 tol upon convergence).
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.

Details

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.

Author(s)

Jorge N. Tendeiro, [e-mail]

References

\insertRef

RobertsLaughlin1996GGUM

\insertRef

Robertsetal2000GGUM

Examples

# Generate data:
gen <- GenData.GGUM(400, 5, 3, "GUM", seed = 139)
# Fit the GUM:
fit <- GUM(gen$data, 3)
# Compare true and estimated item parameters:
cbind(gen$delta, fit$delta)
cbind(c(gen$taus[, 5:7]), c(fit$taus[,  5:7]))

GGUM documentation built on Sept. 8, 2023, 5:38 p.m.