itemfit.rmsea: RMSEA Item Fit

Description

This function estimates a chi squared based measure of item fit in cognitive diagnosis models similar to the RMSEA itemfit implemented in mdltm (von Davier, 2005; cited in Kunina-Habenicht, Rupp & Wilhelm, 2009).

The RMSEA statistic is also called as the RMSD statistic, see IRT.RMSD.

Usage

itemfit.rmsea(n.ik, pi.k, probs, itemnames=NULL)

Value

A list with two entries:

rmsea: Vector of RMSEA item statistics
rmsea.groups: Matrix of group-wise RMSEA item statistics

Arguments

n.ik: An array of four dimensions: Classes x items x categories x groups
pi.k: An array of two dimensions: Classes x groups
probs: An array of three dimensions: Classes x items x categories
itemnames: An optional vector of item names. Default is NULL.

Details

For item $j$, the RMSEA itemfit in this function is calculated as follows: $$ RMSEA_j=\sqrt{ \sum_k \sum_c \pi ( \bold{\theta}_c) \left( P_j ( \bold{\theta}_c ) - \frac{n_{jkc}}{N_{jc}} \right)^2 } $$ where $c$ denotes the class of the skill vector $\bold{\theta}$, $k$ is the item category, $\pi ( \bold{\theta}_c)$ is the estimated class probability of $\bold{\theta}_c$, $P_j$ is the estimated item response function, $n_{jkc}$ is the expected number of students with skill $\bold{\theta}_c$ on item $j$ in category $k$ and $N_{jc}$ is the expected number of students with skill $\bold{\theta}_c$ on item $j$.

References

Kunina-Habenicht, O., Rupp, A. A., & Wilhelm, O. (2009). A practical illustration of multidimensional diagnostic skills profiling: Comparing results from confirmatory factor analysis and diagnostic classification models. Studies in Educational Evaluation, 35, 64--70.