ICC {TestGardener}

Plotting probability and surprisal curves for an item

Description

This is an S3 object that contains information essential plotting probability and surprisal curves for a single multiple choice or rating question. Bin probabilities and surprisal values can also be plotted.

Usage

ICC(x, M, Sfd, Zmat, Pbin, Sbin, Pmatfine, Smatfine, DSmatfine, D2Smatfine,
                PStdErr, SStdErr, ItemArcLen, itemStr=NULL, optStr=NULL)

Arguments

x

An item number.

M

The number of options for this item, including an option for missing or illegal values if required.

Sfd

A functional surprisal curve object defined by K B-spline basis functions and a K by M-1 matrix of coefficients.

Zmat

An M by M-1 matrix satisfying the conditions t(Zmat) Zmat = I and columns sum to zero.

Pbin

A nbin by M matrix of probabilities that a given bin is chosen by a test taker.

Sbin

A nbin by M matrix of surprisal values for the probabilities in Pbin.

Pmatfine

A 101 by M matrix of probability curve values over equally-spaced score index values spanning the interval [0,100].

Smatfine

A 101 by M matrix of surprisal curve values corresponding to the probability values in Pmatfine.

DSmatfine

A 101 by M matrix of first derivative values with respect to score index values for the surprisal values.

D2Smatfine

A 101 by M matrix of second derivative values.

PStdErr

A 101 by M matrix of standard error estimates for the probability curve values.

SStdErr

A 101 by M matrix of standard error estimates for the surprisal curve values.

ItemArcLen

The scope or arc length of the item curve.

itemStr

A string that is the name of the item.

optStr

A character vector containing labels for the item options.

Details

The name ICC for this object is an acronym for the term "item characteristic curve" widely used in the psychometric commuunity.

Function ICC is set up after the initialization process in function make_dataList() has created the members of dataList. Within this list is object SfdList, which cintains a functional data object Sfd for each item. Both the intial coefficient matrices and the subsequent estimates of them are available from Sfd$coefs, and therefore are available in the ICC object. These coefficient matrices are K by M-1 where K is the number of basis functions and M is the number of options for asn item.

Value

The values returned are simply those in the argument list. The S3 ICC object checks each of these and makes available the S3 commands or methods str, print and plot that apply the corresponding ICC versions of these opterations.

Author(s)

Juan Li and James Ramsay

References

Ramsay, J. O., Li J. and Wiberg, M. (2020) Full information optimal scoring. Journal of Educational and Behavioral Statistics, 45, 297-315.

Ramsay, J. O., Li J. and Wiberg, M. (2020) Better rating scale scores with information-based psychometrics. Psych, 2, 347-360.