# ICC: Plotting probability and surprisal curves for an item In TestGardener: Information Analysis for Test and Rating Scale Data

 ICC R Documentation

## 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.

TestGardener documentation built on May 29, 2024, 3:31 a.m.