Calculation of Various Information Functions

Description

This function calculates the information functions associated with the given weights,
and two types of locally optimam weights.

Usage

info_func(param, weight = NULL, npoints = 31, thmin = -4, thmax = 4,
  print = 1, plot = 0, debug = 0)

Arguments

Details

Note that, given category and item weights, information function is defined as
( slope of TRF at theta )^2 / (variance of x at theta)
where TRF and x is calculated with the given set of weights.

In general. the optimal weights depends on the value of theta. Therefore, the name locally optimal weight.
The optimal item weight given category weights is called as locally optimal item weight, or LOW.
When the category weights themselves are optimized it is called as the locally optimal weight, or, LO.
This weight is equivalent to the basic function of Samejima(1969) .

The information function with LO is defined as
∑_j ∑_k (P'_{kj}(θ))^2 / P_{kj}(θ)
where P_{kj}(θ) is the item category response function,
and P'_{kj}(θ) is its derivative.

The information function with LOW is defined as
∑_j (P_j^{*'}(θ))^2 / var(U_j^{*} | θ)
where U_j^{*} = ∑_k v_{kj} U_{kj} is the weighted item score,
and P_j^{*'}(θ) is the derivative of the expected value of U_j^{*} at theta.

Value

A list of
theta theta points
info information function defind as (slope_TRF)^2 / (stdx_t)^2
info_LOW information function with locally optimal item weight
info_LO information function with locally optimal category weight
info_item_LOW item information function with locally optimal item weight
info_item_LO item information function with locally optimal category weight

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. (1969). Estimation of a latent ability using a response pattern of graded scores. Psychometrika Monographs, 34 (Suppl. 4).

Examples

resInfo <- info_func( paramS2, plot=1, print=1 )
resInfo <- info_func( paramS2, weight=weightS21, plot=1, print=0 )
resInfo <- info_func( paramS2, weight=weightS22, plot=1, print=0 )