catR (version 1.1)

nextItem: Selection of the next item

Description

This command selects the next item to be administered, given the list of previously administered items and the current ability estimate, with the 'maximum information' criterion.

Usage

nextItem(itemBank, theta, out=NULL, method="info")

Arguments

itemBank

an item bank of class itBank as output of the function createItemBank.

theta

numeric: the current value of the ability estimate.

out

either a vector of integer values specifying the items previously administered, or NULL (default).

method

character: the method for next item selection, either "info" (default) or "Owen". See Details.

Value

• A list with three arguments:
• item
  the selected item (identified by its number in the item bank).
• par
  the vector of item parameters of the selected item.
• info
  the value of the information function for the selected item and the current ability estimate.
• method
  the value of the method argument.

Details

Currently two methods are available for selecting the next item to be administered in the adaptive test. For a given current ability estimate, the next item is selected (among the available items) either using the information criterion or using Owen's procedure (Owen, 1975). The information criterion selects the next item as the one which maximizes the item information function (Baker, 1992). The most informative item is selected from the table of item informations provided by the bank of items specified with itemBank. Owen's procedure consists in selecting as next the item whose difficulty level is closest to the current ability estimate. Under the 1PL model, both methods are equivalent. The method for next item selection is specified by the method argument. Possible values are "info" for the information criterion, and "Owen" for Owen's method. Other values return an error message. The available items are those that are not specified in the out argument. By default, out is NULL, which means that all items are available.

References

Baker, F.B. (1992). Item response theory: parameter estimation techniques. New York, NY: Marcel Dekker. Owen, R. J. (1975). A Bayesian sequential procedure for quantal response in the context of adaptive mental testing. Journal of the American Statistical Association, 70, 351-356.

See Also

createItemBank

Examples

# Loading the 'tcals' parameters 
 data(tcals)
 tcals <- as.matrix(tcals)
 
 # Item bank creation with 'tcals' item parameters
 bank <- createItemBank(tcals)

 ## Information criterion

 # Selecting the next item, current ability estimate is 0
 nextItem(bank, 0) # item 63 is selected

 # Selecting the next item, current ability estimate is 0
 # and item 63 is removed
 nextItem(bank, 0, out=63) # item 10 is selected

 # Selecting the next item, current ability estimate is 0
 # and items 63 and 10 are removed
 nextItem(bank, 0, out=c(63,10)) # item 62 is selected

 ## Owen's method

 # Selecting the next item, current ability estimate is 0
 nextItem(bank, 0, method="Owen") # item 24 is selected

 # Selecting the next item, current ability estimate is 0
 # and item 24 is removed
 nextItem(bank, 0, out=24, method="Owen")