CDM (version 7.4-19)

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 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

Value

stats

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

Details

Let \(P_j( \alpha _l)\) the estimated item response function for the GDINA model and \(\hat{P}_j( \alpha _l)\) the item response model for the approximated model (DINA, DINO or ACDM). The unweighted distance uwgtdist as a measure of misfit is defined as $$uwgtdist=\frac{1}{2^K} \sum_l ( P_j( \alpha _l) - \hat{P}_j( \alpha _l) )^2$$ The weighted distance wgtdist measures the discrepancy with respected to the probabilities \(w_l=P( \alpha_l)\) of estimated skill classes $$wgtdist=\sum_l w_l (P_j( \alpha _l) - \hat{P}_j( \alpha _l) )^2$$

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.

See Also

See the GDINA::modelcomp function in the GDINA package for similar functionality.

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") )
# }