index2info {TestGardener}

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.

See Also

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
  oldpar <- par(no.readonly=TRUE)
  Scope_plot(infoList$infoSurp, infoList$infoSurpvec)
  par(oldpar)