index2info | R Documentation |

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.

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

`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 |

`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 |

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 |

`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 |

Juan Li and James Ramsay

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`

```
# 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)
```

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