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

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).

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

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 $$wgtdist=\sum_l w_l (P_j( \alpha _l) - \hat{P}_j( \alpha _l) )^2$$

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