itemfit.rmsea {CDM} | R Documentation |

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.

This function is used in `din`

, `gdina`

and
`gdm`

.

[Package *CDM* version 7.5-15 Index]