itemfit.rmsea {CDM}

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)

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.

Value

A list with two entries:

rmsea

Vector of RMSEA item statistics

rmsea.groups

Matrix of group-wise RMSEA item statistics

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.

See Also

This function is used in din, gdina and gdm.