bootCRM function

Computing Standard Errors for Item Parameter Estimates using Bootstrap Sampling

Computes the standard errors of item parameter estimates using a non-parametric bootstrapping approach

bootCRM(data,max.item,min.item,max.EMCycle=500,converge=.01,
        type="Shojima",BFGS=TRUE,nsample=50)

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.
• max.item: a vector of length m indicating the maximum possible score for each item.
• min.item: a vector of length m indicating the minimum possible score for each item.
• max.EMCycle: a number of maximum EM Cycles used in the iteration. Default is 500.
• converge: a criteria value indicating the difference between loglikelihoods of two consecutive EM cycles to stop the iteration. Default is .01
• type: type of optimization. Default is the non-iterative EM developed by Shojima(2005).
• BFGS: a valid argument when type is equal to "Wang&Zeng". If TRUE, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is used to update Hessian.
• nsample: a number of bootstrap samples used in estimating the standard errors. Default is 50

Details

bootCRM computes the standard errors of item parameter estimates using a non-parametric bootstrap sampling approach.

Returns

bootCRM returns a list with three elements. Each element of the list is an mx3 matrix where m is the number of items. The first column includes the item parameter estimates from the original sample, the second column includes the average item parameter estimates from R bootstrap samples (the mean of the empirical sampling distribution), and the third column includes the standard errors of the item parameter estimates obtained from bootstrap samples (standard deviation of the empirical sampling distribution).

• Discrimination: Estimates for item discriminations

• Difficulty: Estimates for item difficulties

• Alpha: Estimates for alpha parameters

Author(s)

Cengiz Zopluoglu

Note

It may make take too long to get the results if you request a large number of bootstrap samples. By default, the number of bootstrap samples is 50, and it takes a couple minutes for the sample datasets provided in the package. It would be a good idea to try 100 or 500 bootstrap samples if you have enough time.

See Also

EstCRMitem for estimating item parameters, EstCRMperson for estimating person parameters, fitCRM for computing item-fit statistics and drawing empirical 3D item response curves, plotCRM for drawing theoretical 3D item category response curves,

Examples

## Not run:

  
  ##load the dataset EPIA
  data(EPIA)
  
  bootCRM(data=EPIA,
  max.item=c(112,112,112,112,112),
  min.item=c(0,0,0,0,0),
  max.EMCycle=200,
  converge=.01,
  nsample=100)
  
  
  ##load the dataset SelfEff
  data(SelfEff)
  
  bootCRM(data=SelfEff,
  max.item=c(11,11,11,11,11,11,11,11,11,11),
  min.item=c(0,0,0,0,0,0,0,0,0,0),
  max.EMCycle=200,
  converge=.01,
  nsample=100)
## End(Not run)