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 several possible criteria.

Usage

nextItem(itemBank, theta, out=NULL, x=NULL, criterion="MFI",
 	method="BM", priorDist="norm", priorPar=c(0,1), D=1,
 	range=c(-4,4), parInt=c(-4,4,33), infoType="observed")

Arguments

itemBank

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

theta

numeric: the current value of the ability estimate (default is 0).

out

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

numeric: the provisional response pattern, with the same length as out (and NULL by default). Ignored if method is either "MFI" or "Owen". See Details.

criterion

character: the method for next item selection. Possible values are "MFI" (default), "Owen" "MLWI", "MPWI", "MEI", "MEPV" and random. See Details<

method

character: the ability estimator. Possible values are "BM" (default), "ML" and "WL". See Details.

priorDist

character: the prior ability distribution. Possible values are "norm" (default) for the normal distribution, and "unif" for the uniform distribution. Ignored if type is not "MPWI".

priorPar

numeric: a vector of two components with the prior parameters. If priorDist is "norm", then priorPar contains the mean and the standard deviation of the normal distribution. If priorDist

numeric: the metric constant. Default is D=1 (for logistic metric); D=1.702 yields approximately the normal metric (Haley, 1952).

range

numeric: vector of two components specifying the range wherein the ability estimate must be looked for (default is c(-4,4)). Ignored if method=="EAP".

parInt

numeric: a vector of three numeric values, specifying respectively the lower bound, the upper bound and the number of quadrature points for numerical integration (default is c(-4,4,33)). Ignored if method is eithe

infoType

character: the type of information function to be used. Possible values are "observed" (default) for observed information function, and "Fisher" for Fisher information function. Ignored if criterion

Value

A list with three arguments:
itemthe selected item (identified by its number in the item bank).
parthe vector of item parameters of the selected item.
infothe value of the MFI, Fisher's information, the MLWI, the MPWI, the MEI, the EPV,or NA (for "random" criterion) for the selected item and the current ability estimate.
criterionthe value of the criterion argument.

Details

Currently seven 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) by using: the maximum Fisher information (MFI) criterion, the maximum likelihood weighted information (MLWI) (Veerkamp and Berger, 1997), the maximum posterior weighted information (MPWI) (van der Linden, 1998), Owen's procedure (Owen, 1975), the maximum expected information (MEI) criterion (van der Linden, 1998), the minimum expected posterior variance (MEPV) or by selecting the next item completely randomly among the available items. The MFI 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 Owen and MFI methods are equivalent. The MLWI and MPWI criteria select the next item as the one with maximal information, weighted either by the likelihood function or the posterior distribution. See the function MWI for further details. Finally, the MEI criterion selects the item with maximum expected information, computed with the MEI function. The method for next item selection is specified by the criterion argument. Possible values are "MFI" for maximum Fisher information criterion, "Owen" for Owen's method, "MLWI" for maximum likelihood weighted information criterion, "MPWI" for the maximum posterior weighted information criterion, "MEI" for the maximum expected information criterion, "MEPV" for minimum expected posterior variance, and "random" for random selection. Other values return an error message. For MFI, MEI and Owen criteria, the provisional ability estimate must be supplied throught the theta argument (by default, it is equal to zero). For MLWI and MPWI criteria, this argument is ignored. 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. For MEI, MEPV, MLWI and MPWI methods, the provisional response pattern must be provided through the x argument. It must be of 0/1 entries and of the same length as the out argument. It is ignored with MFI and Owen criteria. Moreover, the range of integration (or posterior variance computation) is specified by the triplet parInt, where the first, second, and third value correspond to the arguments lower, upper and nqp of the MWI function, respectively. The method, priorDist, priorPar, D, range and intPar arguments fix the ability estimator. See the thetaEst function for further details. Finally, for MEI criterion, the type of information function must be supplied through the infoType argument. It is equal to "observed" by default, which refers to the observed information function, and the other possible value is "Fisher" for Fisher information function. See the MEI funtion for further details. This argumpent is ignored if criterion is not "MEI".

References

Baker, F.B. (1992). Item response theory: parameter estimation techniques. New York, NY: Marcel Dekker. Choi, S. W., and Swartz, R. J. (2009). Comparison of CAT item selection criteria for polytomous items. Applied PScyhological Measurement, 32, 419-440. 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. van der Linden, W. J. (1998). Bayesian item selection criteria for adaptive testing. Psychometrika, 63, 201-216. van der Linden, W. J., and Pashley, P. J. (2000). Item selection and ability estimlation in adaptive testing. In W. J. van der Linden and C. A. W. Glas (Eds.), Computerized adaptive testing. Theory and practice (pp. 1-25). Boston, MA: Kluwer. Veerkamp, W. J. J., and Berger, M. P. F. (1997). Some new item selection criteria for adaptive testing. Journal of Educational and Behavioral Statistics, 22, 203-226.

Examples

Run this code

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

 ## MFI 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, criterion="Owen") # item 24 is selected

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

 # Selecting the next item, current response pattern is 0
 # and item 63 was administered first
 nextItem(bank, x=0, out=63, criterion="MLWI") 
 nextItem(bank, x=0, out=63, criterion="MPWI")

 # Selecting the next item, current response pattern is
 # (0,1) and item 19 is removed
 nextItem(bank, x=c(0,1), out=c(63, 19), criterion="MLWI")
 nextItem(bank, x=c(0,1), out=c(63, 19), criterion="MPWI")

 ## MEI method

 # Selecting the next item, current response pattern is 0
 # and item 63 was administered first
 nextItem(bank, x=0, out=63, criterion="MEI") 

 # With Fisher information
 nextItem(bank, x=0, out=63, criterion="MEI", infoType="Fisher")

 ## MEPV method

 # Selecting the next item, current response pattern is 0
 # and item 63 was administered first
 nextItem(bank, x=0, out=63, criterion="MEPV") 

 ## Random method

 # Selecting the next item, item 63 was administered first
 nextItem(bank, out=63, criterion="random") 
 nextItem(bank, out=63, criterion="random")  # may produce a 
                                             # different result

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