GGUM: Fit the generalized graded unfolding model (GGUM)

In GGUM: Generalized Graded Unfolding Model

Fit the generalized graded unfolding model (GGUM)

Description

GGUM estimates all item parameters for the GGUM.

Usage

GGUM(
  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 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 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	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 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 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.

Author(s)

Jorge N. Tendeiro, [e-mail]

References

\insertRef

RobertsLaughlin1996GGUM

\insertRef

Robertsetal2000GGUM

Examples

## 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)

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