fitCRM: Compute item fit residual statistics for the Continuous... In EstCRM: Calibrating Parameters for the Samejima's Continuous IRT Model

Description

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

Usage

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

Arguments

 `data` a data frame with N rows and m columns, with N denoting the number of subjects and m denoting the number of items. `ipar` a matrix with m rows and three columns, with m denoting the number of items. The first column is the a parameters, the second column is the b parameters, and the third column is the alpha parameters `est.thetas` object of class "`CRMtheta`" obtained by using `EstCRMperson()` `max.item` a vector of length m indicating the maximum possible score for each item. `group` an integer, number of ability groups to compute item fit residual statistics. Default 20.

Details

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:

Please see the manual for the equation!

Value

 `fit.stat` a data frame with k rows and m+1 columns with k denoting the number of ability intervals and m denoting the number of items. The first column is the ability interval. Other elements are the standardized residuals of item m in ability interval k. `emp.irf` a list of length m with m denoting the number of items. Each element is a 3D plot representing the item category response curve based on the empirical probabilities. See examples below.

Cengiz Zopluoglu

References

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.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39``` ```##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 ```