itemfit.rmsea {CDM} | R Documentation |
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 |
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
.