RMSEA Item Fit
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.
itemfit.rmsea(n.ik, pi.k, probs, itemnames=NULL)
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 |
For item j, the RMSEA itemfit in this function is calculated as follows:
RMSEA_j=√{ ∑_k ∑_c π ( \bold{θ}_c) ≤ft( P_j ( \bold{θ}_c ) - \frac{n_{jkc}}{N_{jc}} \right)^2 }
where c denotes the class of the skill vector \bold{θ}, k is the item category, π ( \bold{θ}_c) is the estimated class probability of \bold{θ}_c, P_j is the estimated item response function, n_{jkc} is the expected number of students with skill \bold{θ}_c on item j in category k and N_{jc} is the expected number of students with skill \bold{θ}_c on item j.
A list with two entries:
rmsea |
Vector of RMSEA item statistics |
rmsea.groups |
Matrix of group-wise RMSEA item statistics |
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.
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