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).Usage
itemfit.rmsea(n.ik, pi.k, probs, itemnames=NULL)
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 four dimensions: Classes x items x categories x groups
itemnames
An optional vector of item names. Default is NULL.
Value
- A list with two entries:
- rmseaVector of RMSEA item statistics
- rmsea.groupsMatrix of group-wise RMSEA item statistics
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.
von Davier, M. (2005). A general diagnostic model applied to language
testing data. ETS Research Report RR-05-16. ETS, Princeton, NJ: ETS.