fitCRM {EstCRM} | R Documentation |

Compute item fit residual statistics for the Continuous Response Model as described in Ferrando (2002)

```
fitCRM(data, ipar, est.thetas, max.item,group)
```

`data` |
a data frame with |

`ipar` |
a matrix with |

`est.thetas` |
object of class " |

`max.item` |
a vector of length |

`group` |
an integer, number of ability groups to compute item fit residual statistics. Default 20. |

The function computes the item fit residual statistics as decribed in Ferrando (2002). The steps in the procedure are as the following:

1- Re-scaled *θ* estimates are obtained.

2- *θ* estimates are sorted and assigned to *k* intervals on the *θ* continuum.

3- The mean item score is computed in each interval for each of the items.

4- The expected item score and the conditional variance in each interval are obtained with the item parameter estimates and taking the median theta estimate for the interval.

5- An approximate standardized residual for item *m* at ability interval *k* is obtained as:

```
z_{mk}= \frac{\bar{X}_{mk} - E(X_{m}|\theta_{k})}{\sqrt{\frac{\sigma^2(X_{m}|\theta_{k})}{N_{k}}}}
```

`fit.stat` |
a data frame with |

`emp.irf` |
a list of length |

Cengiz Zopluoglu

Ferrando, P.J.(2002). Theoretical and Empirical Comparison between Two Models for Continuous Item Responses. *Multivariate Behavioral Research*, 37(4), 521-542.

`EstCRMperson`

for estimating person parameters,
`EstCRMitem`

for estimating item parameters
`plotCRM`

for drawing theoretical 3D item category response curves,
`simCRM`

for generating data under CRM.

```
##load the dataset EPIA
data(EPIA)
##Due to the run time issues for examples during the package building
##I had to reduce the run time. So, I run the fit analysis for a subset
##of the whole data, the first 100 examinees. You can ignore the
##following line and just run the analysis for the whole dataset.
##Normally, it is not a good idea to run the analysis for a 100
##subjects
EPIA <- EPIA[1:100,] #Please ignore this line
##Define the vectors "max.item" and "min.item". The maximum possible
##score was 112 and the minimum possible score was 0 for all items
max.item <- c(112,112,112,112,112)
min.item <- c(0,0,0,0,0)
##Estimate item parameters
CRM <- EstCRMitem(EPIA, max.item, min.item, max.EMCycle = 500, converge = 0.01)
par <- CRM$param
##Estimate the person parameters
CRMthetas <- EstCRMperson(EPIA,par,min.item,max.item)
##Compute the item fit residual statistics and empirical item category
##response curves
fit <- fitCRM(EPIA, par, CRMthetas, max.item,group=10)
##Item-fit residual statistics
fit$fit.stat
##Empirical item category response curves
fit$emp.irf[[1]] #Item 1
```

[Package *EstCRM* version 1.4 Index]