# index2info: Compute results using arc length or information as the... In TestGardener: Information Analysis for Test and Rating Scale Data

 index2info R Documentation

## Compute results using arc length or information as the abscissa.

### Description

The one-dimensional psychometric model defines a space curve within the vector space defined by the total collection of option surprisal curves. This curve is a valuable resource since positions along the curve are defined in bits and positions on the curve are subject to the same strict properties that apply to physical measurements.

Function `index2info` is required to convert objects defined over the score index continuum `c(0,100)` to the same objects over the arc length continuum `c(0,infoSurp)`, and also vice versa. Since the arc length or information continuum is along a space curve that is invariant under strictly monotone transformations of the score index `index`, and is also a metric, it is an ideal choice for the abscissa in all plots.

### Usage

``````   index2info(index, Qvec, SfdList, binctr, itemindex=1:n, plotrng=c(0,100),
shortwrd)
``````

### Arguments

 `index` A vector of score index, test score, or arc length values, one for each examinee or respondent. `Qvec` A vector of locations of the five marker percentages. `SfdList` A numbered list object produced by a TestGardener analysis of a test. Its length is equal to the number of items in the test or questions in the scale. Each member of `SfdList` is a named list containing information computed during the analysis. `binctr` A vector of locations of the bin centers. `itemindex` A vector containing the indices of the items to be used. `plotrng` A vector of length 2 containing the starting score index and end score index values of the range to be plotted. `shortwrd` If TRUE only vectors infoSurp and infoSurpvec are returned in order to speed up the computation within cycles in function `Analyze()` where only these objects are required. The default is FALSE.

### Value

A named list object containing these results of the analysis:

 `infoSurp` The length of the test information or scale curve. `infoSurpvec` Positions on the test information or scale curve corresponding to a fine mesh of score index values (typically 101 values between 0 and 100). `infoSurpfd` Functional data object representing the relation between the score index abscissa and the infoSurp or information ordinate. `scopevec` A vector of positions on the test information or scale curve corresponding to the input score index values in argument `index`. `Qvec_al` Values in arc length of the five marker percentages. `binctr_al` Values in arc length of the bin centers. `Sfd.info` A functional data object representing the relation between the infoSurp or information abscissa and the score index ordinate. `Sdim.index` The dimension of the overspace, which equal to sum of the number of options in the items specified in `itemindex`.

### 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.

`Analyze`

### Examples

``````  #  Example 1.  Display the scope or information curve for the
#  short SweSAT multiple choice test with 24 items and 1000 examinees.
#  The scope curve is constructed using the complete analysis cycles.
#  Set up the required arguments using the converged parmList object.
indfine     <- seq(0,100,len=101)
index       <- Quant_13B_problem_parmList\$index
Qvec        <- Quant_13B_problem_parmList\$Qvec
SfdList     <- Quant_13B_problem_parmList\$SfdList
binctr      <- Quant_13B_problem_parmList\$binctr
#  Carry out the construction of the information results.
infoList    <- index2info(index, Qvec, SfdList, binctr)
# Plot the shape of the information curve