iif {lazy.irt}

R Documentation

Calculation of Information Functions

Description

This function calculates Test (tif), Item (iif) and Item Category (icif) Information Functions.
Japanese help file: (iif_JPH)

Usage

iif(
  param,
  theta = NULL,
  npoints = 31,
  thmin = -4,
  thmax = 4,
  legend = 1,
  maxinfo = 0,
  numderiv = 0,
  smallP = 1e-09,
  print = 1,
  plot = 0,
  debug = 0
)

Arguments

param	Item Parameter Data Frame.
theta	Discrete theta values
npoints	# of discrete points for theta.
thmin	Minimum value of discrete thata value.
thmax	Maximum value of discrete thata value.
legend	= 0 to skip printing legend.
maxinfo	= The maximum value of item information function for plot.
numderiv	= 1 to use numerical first derivatives of irf.
smallP	Minimum value of probability in irf and dirf functions.
print	= 1 to print the summary = 2 to print test information functions. = 3 to print item information functions. = 4 to print item category information functions.
plot	= 1 to plot test information functions = 2 to plot item information functions. = 3 to plot the locally best item and item categorie weights.
debug	= 1 to print intemediate result.

Details

The item category information function, icif, (item response information function) is defined as
I_{kj}(\theta) = (P'_{kj}(\theta))^2 / P_{kj}(\theta) - P''_{kj}(\theta)
where P_{kj}(\theta) is the item category response function and P'_{kj}(\theta) is the first derivative of P_{kj}(\theta).
The second derivatives, P''_{kj}(\theta) , will be calculated numerically by dirt_num using lazy.mat::JacobianMat.

The item information function, iif, is defined as
I_j(\theta) = \sum_k I_{kj}(\theta) = \sum_k (P'_{kj}(\theta))^2 / P_{kj}(\theta)
The test information function, if, is the sum of the above:
I(\theta) = \sum_j I_j(\theta) = \sum_j \sum_k (P'_{kj}(\theta))^2 / P_{kj}(\theta) .

Note that \sum_k P_{kj}(\theta) = 1 and \sum_k P'_{kj}(\theta) = \sum_k P''_{kj}(\theta) = 0 .

Above corresponds to the information functions from info_func or obscore associated with locally best item category weights (LO).

Value

A list of

theta: theta points
fromP, toP: location of each item category in item info
TRF: test response function (tcc)
icrf: item category response functions
dicrf: derivative of icrf
info: test information function (if)
info_item: item information function (iif)
info_item_cat: item category information function (icif)

References

Birnbaum, A.(1968) Some Latent Traint Models. In F. M. Lord and M. R. Novick, Statistical Theories of Mental Test Scores. Reading, Mass.: Addison-Wesley.

Samejima, F. (2010). The General Graded Response Model. (p79-80) In Nering, M. L. and Ostini, R. Eds. Handbook of Polytomous Item Response Theory Models. NY, NY: Routledge

Samejima, F. (1969). Estimation of a latent ability using a response pattern of graded scores. (Eq 6-6 in p39) Psychometrika Monographs, 34 (Suppl. 4).

Examples

resInfo <- iif( paramA1, plot=4, print=4 )

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