catR (version 1.2)

createItemBank: Item bank generation

Description

This command creates an item bank from a matrix of item parameters. Item information functions are evaluated for all items and a fine grid of ability levels, to be supplied.

Usage

createItemBank(items=100, model="4PL", thMin=-4, thMax=4,
	 step=0.01, seed=1, D=1)

Arguments

items

either an integer value or a matrix of item parameters. See Details.

model

character: the name of the logistic IRT model, with possible values "1PL", "2PL", "3PL" or "4PL" (default). Ignored if items is a matrix.

thMin

numeric: the lower bound for the fine grid of ability levels (default is -4). See Details.

thMax

numeric: the upper bound for the fine grid of ability levels (default is 4). See Details.

step

numeric: the step value for the fine grid of ability levels (default is 0.01). See Details.

seed

numeric: the random seed number for the generation of item parameters (default is 1). See set.seed for further details.

D

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

Value

• A list of class "itBank" with three arguments:
• itemPar
  the matrix of item parameters, either provided by items or generated.
• theta
  a vector with the ability levels of the fine grid, defined by arguments thMin, thMax and step.
• infoTab
  a matrix of Fisher information functions, evaluated for each ability level (one row per ability level) and each item (one column per item).

Details

If items is a matrix, it has the following format: one row per item and four columns, with respectively the discrimination $a_i$, the difficulty $b_i$, the pseudo-guessing $c_i$ and the inattention $d_i$ parameters (Barton and Lord, 1981). If items is an integer, it corresponds to the number of items to be included in the item bank. Corresponding item parameters are (by default) randomly drawn from the following distributions: $a_i \sim N(1, 0.2^2)$, $b_i \sim N(0, 1)$, $c_i \sim U([0, 0.25])$ and $d_i \sim U([0.75, 1])$. Inattention parameters $d_i$ are fixed to 1 if model is not "4PL"; pseudo-guessing parameters $c_i$ are fixed to zero if model is either "1PL" or "2PL"; and discrimination parameters $a_i$ are fixed to 1 if model="1PL". The random generation of item parameters can be controlled by the seed argument. The item bank consists of the(infoTab) matrix, which holds Fisher information functions (Baker, 1992), evaluated for each item in the bank and at each value of a sequence of ability levels. These abilities are ranging from thMin to thMax by steps of step units. The returned list contains in addition the sequence of ability levels and the matrix of item parameters.

References

Baker, F.B. (1992). Item response theory: parameter estimation techniques. New York, NY: Marcel Dekker. Barton, M.A., and Lord, F.M. (1981). An upper asymptote for the three-parameter logistic item-response model. Research Bulletin 81-20. Princeton, NJ: Educational Testing Service. Haley, D.C. (1952). Estimation of the dosage mortality relationship when the dose is subject to error. Technical report no 15. Palo Alto, CA: Applied Mathematics and Statistics Laboratory, Stanford University.

See Also

Ii

Examples

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

 # Changing the fine grid of ability levels
 createItemBank(tcals, thMin=-2, thMax=2, step=0.05)

 # Item bank creation with 500 items
 createItemBank(items=500)