CDM: gdina.wald – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

gdina.wald

Wald Statistic for Item Fit of the DINA and ACDM Rule for GDINA Model

Description

This function tests with a Wald test for the GDINA model whether a DINA or a ACDM condensation rule leads to a sufficient item fit compared to the saturated GDINA rule (de la Torre & Lee, 2013). The Wald test is accompanied by the RMSEA fit and weighted and unweighted distance measures (wgtdist, uwgtdist), see Details (compare Ma, Iaconangelo, & de la Torre, 2016).

Usage

gdina.wald(object)

## S3 method for class 'gdina.wald'
summary(object, digits=3,
    vars=c("X2", "p", "sig", "RMSEA", "wgtdist"),  ...)

Arguments

`object`	A fitted `gdina` model
`digits`	Number of digits after decimal used for rounding.
`vars`	Vector including variables which should be displayed in `summary`. See the output `stats`.
`...`	Further arguments to be passed

Details

Let P_j( α _l) the estimated item response function for the GDINA model and \hat{P}_j( α _l) the item response model for the approximated model (DINA, DINO or ACDM). The unweighted distance uwgtdist as a measure of misfit is defined as

uwgtdist=\frac{1}{2^K} ∑_l ( P_j( α _l) - \hat{P}_j( α _l) )^2

The weighted distance wgtdist measures the discrepancy with respected to the probabilities w_l=P( α_l) of estimated skill classes

wgtdist=∑_l w_l (P_j( α _l) - \hat{P}_j( α _l) )^2

Value

stats

Data frame with Wald statistic for every item, corresponding p values and a RMSEA fit statistic

References

de la Torre, J., & Lee, Y. S. (2013). Evaluating the Wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355-373.

Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection, and attribute classification. Applied Psychological Measurement, 40(3), 200-217.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Wald test for DINA simulated data sim.dina
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

# Model 1: estimate GDINA model
mod1 <- CDM::gdina( sim.dina, q.matrix=sim.qmatrix,  rule="GDINA")
summary(mod1)

# perform Wald test
res1 <- CDM::gdina.wald( mod1 )
summary(res1)
# -> results show that all but one item fit according to the DINA rule

# select some output
summary(res1, vars=c("wgtdist", "p") )

## End(Not run)

CDM

Cognitive Diagnosis Modeling

v7.5-15

GPL (>= 2)

Authors

Alexander Robitzsch [aut, cre], Thomas Kiefer [aut], Ann Cathrice George [aut], Ali Uenlue [aut]

Initial release

2020-03-10 14:19:21