GGUM-package {GGUM} | R Documentation |
GGUM
Description
The GGUM
package fits the generalized graded response
model (GGUM; Roberts et al., 1996, 2000). It is based on marginal maximum
likelihood (Roberts et al., 2000) to estimate the item parameters and an
estimated a posteriori (EAP) method to estimate the person parameters.
The GGUM is defined 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
andn
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 personn
. -
\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
.
This package produces comparable results to the ones based on the GGUM2004 program (Roberts et al., 2000; Roberts et al., 2006), for the GUM (Model 3 in GGUM2004) and the GGUM (Model 8 in GGUM2004). For those accustomed to using GGUM2004, this packages provides a useful set of functions that allow exporting data and code to GGUM2004, running GGUM2004, and retrieving the parameter estimates. Thus, if desired, one can run GGUM2004 and retrieve the results completely from within the R environment.
Versions:
Version 0.3.1 (January 2018)
Version 0.3.2 (July 2018)
Fixed a bug related to data preprocessing (removing response patterns with all-disagree answers). Many thanks to JB Duck-Mayr for offering a fix in GitHub, and also to Michael Hermann who independently spotted the same issue (for dichotomous data).Version 0.4 (January 2020)
Fixed two bugs (in Theta.EAP() and write.GGUM2004())Version 0.4-1 (May 2020)
Implemented two changes in GUM.R to adapt to R 4.1 (currently R-devel) and survive CRAN's build checks.Version 0.4-2 (February 2021)
Updated affiliation.Version 0.4-3 (October 2021)
Implemented further changes to adapt to R 4.1, similar to what was done in Version 0.4-1.Version 0.5 (September 2023)
Updated some functions to fix a bug related to identifying the class of objects.
Details
Package: | GGUM |
Type: | Package |
Version: | 0.5 |
Date: | 2023-09-08 |
License: | GPL Version 2 or later |
The GGUM package contains useful functions, summarized below:
Fitting the GUM/GGUM:
Function Description GenData.GGUM
Generate data from the GUM/GGUM probs.GGUM
Compute model probabilities for the GGUM GUM
Fit the GUM GGUM
Fit the GGUM MODFIT
MODFIT for the GGUM Theta.EAP
Estimate thetas and their SEs (GUM, GGUM) Plots:
Function Description plotCRC
Plot item category response curves (CRCs) plotICC
Plot item characteristic curves (ICCs) plotIIF
Plot item information functions (IIFs) plotTCC
Plot test characteristic curve (TCC) plotTIF
Plot test information function (TIF) GGUM2004 interface:
Function Description export.GGUM2004
Exports data in GGUM2004 friendly format write.GGUM2004
Writes a command file for GGUM2004 run.GGUM2004
Call GGUM2004 and import the estimated parameters into R read.item.GGUM2004
Read GGUM2004 item estimates into R read.person.GGUM2004
Read GGUM2004 person estimates into R Available methods for objects of class "GGUM":
plot() print() summary()
Author(s)
Maintainer: Jorge N. Tendeiro tendeiro@hiroshima-u.ac.jp
Authors:
Sebastian Castro-Alvarez secastroal@gmail.com
References
Roberts JS, Laughlin JE (1996). “A unidimensional item response theory model for unfolding responses from a graded disagree-agree response scale.” Applied Psychological Measurement, 20, 231-255.
Roberts JS, Donoghue JR, Laughlin JE (2000). “A general item response theory model for unfolding unidimensional polytomous responses.” Applied Psychological Measurement, 24, 3-32.
Roberts JS, Fang H, Cui W, Wang Y (2006). “GGUM2004: A Windows-Based Program to Estimate Parameters in the Generalized Graded Unfolding Model.” Applied Psychological Measurement, 30, 64-65.
See Also
Useful links:
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$data, 2)
th1 <- Theta.EAP(fit1)
# Plot the test information function:
plotTIF(fit1, th1)
# Check model fit:
MOD.res <- MODFIT(fit1)
# Example 2 - Different C across items:
# Generate data:
set.seed(1); C <- sample(3:5, 10, replace = TRUE)
I <- 10
gen2 <- GenData.GGUM(2000, I, C, seed = 125)
# Fit the GGUM:
fit2 <- GGUM(gen2$data, C)
th2 <- Theta.EAP(fit2)
# Plot item information functions for items 1 and 3:
plotIIF(fit2, th2, items = c(1, 3))
# Example 3 - Fit GGUM using GGUM2004:
# Assuming the installation directory is C:/GGUM2004, then do this:
# Export data to GGUM2004:
export.GGUM2004(gen2$data)
# Write command file:
write.GGUM2004(I, C)
# Run GGUM2004:
res.GGUM2004 <- run.GGUM2004()
## End(Not run)