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 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 " |
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. |
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 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
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