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`

.

*CDM*version 8.2-6 Index]