TG_analysis: Statistics for Multiple choice Tests, Rating Scales and Other Choice Data)

Description

Given an choice ingter-valued index matrix and a vector of numbers of item options, the function cycles through a set of iterations involving surprisal curve estimation followed by test taker index values.

Usage

TG_analysis(chcemat, scoreList, noption, sumscr_rng=NULL, 
              titlestr=NULL, itemlabvec=NULL, optlabList=NULL,
              nbin=nbinDefault(N), NumBasis=7, NumDensBasis=7,
              jitterwrd=TRUE, PcntMarkers=c( 5, 25, 50, 75, 95),
              ncycle=10, itdisp=FALSE, verbose=FALSE)

Value

Four list objects, each containing objects that are required for various displays, tables and other results:

parmList: A list object containing objects useful for displaying results that involve the score index cotninuum:

SfdList: A list object of length n, each containing objects for an item for displaying that item's surprisal curves as defined by the score index values after the analysis. See the help page for function Analyze for a description of these objects.
Qvec: A vector containing the positions on the score index continuum of the marker percentages defined in the arguments of function make_dataList().
binctr: A vector of length nbin containing the positions on the score index continuum of the bin centres.
indexScore: A vector of length N containing the positions on the score index contiuum of each person.
infoSurp: The length of the test or scale information continuum in M-bits.

infoList: A list object containing objects useful for displaying results that involve the scale information cotninuum:

infofine: A fine mesh of 101 values that is used to plot the scale information comntinuum.
scopevec: A vector of length N containing the positions on the scale information contiuum of each person.
Qinfovec: A vector containing the positions on the scale information continuum of the marker percentages defined in the arguments of function make_dataList().
infobinctr: A vector of length nbin containing the positions on the scale information continuum of the bin centres.

HALsave: A ncycle by 2 matrix containing in the first column the data fit values and in the second column the infoSurp or arclength values.
analysisListvec: A list of length ncycle containing the parmList object for each cycle.

Arguments

chcemat: An N by n matrix. Column i must contain the integers from 1 to M_i, where M_i is the number of options for item i. If missing or illegitimate responses exist for item i, the column must also contain an integer greater than M_i that is used to identify such responoses. Alternatively, the column use NA for this purpose. Because missing and illegible responses are normally rare, they are given a different and simpler estimation procedure for their surprisal values. U is mandatory.
scoreList: Either a list of length n, each containing a vector of length M_i that assigns numeric weights to the options for that item. In the special case of multiple choice items where the correct option has weight 1 and all others weight 0, a single integer can identify the correct answer. If all the items are of the multiple type, scoreList may be a numeric vector of length n containing the right answer indices. List object scoreList is mandatory because these weights define the person scores for the surprisal curve estimation process.
noption: A numeric vector of length n containing the number of options for each item.
sumscr_rng: A vector of length 2 indicating the initial and final sum score values. Default is NULL the whole sum score is used.
titlestr: A title string for the data and their analyses. Default is NULL.
itemlabvec: A character value containing labels for the items. Default is NULL and item position numbers are used.
optlabList: A list vector of length n, each element i of which is a character vector of length M_i. Default is NULL, and option numbers are used.
nbin: The number of bins containing proportions of choices.
NumBasis: The number of spline basis functions to use for surprisal values. Defaults to 7.
NumDensBasis: The number of spline basis functions to use for score probability density function. Defaults to 7.
jitterwrd: A logical object indicating whether a small jittering perturbation should be used to break up ties. Defaults to TRUE.
PcntMarkers: A vector of percentages inside of [0,100] that appear in plots. Defaults to c(5, 25, 50, 75, 95). Extra displays are provided. Defaults to FALSE.
ncycle: The number of cycles in the analysis. Defaults to 10.
itdisp: Display results for function theta_fun.
verbose: Extra displays are provided. Defaults to FALSE.

Author

Juan Li and James Ramsay

Details

This function in package TestGardener processes at a mininum two objects: (1) A matrix chcemat that contains indices of choices made in a sequence of choice situations (its number columns n) by a set of persons making the choices (its number of rows N); and (2) A list vector scoreList of length n containing numerical weights or scores for each choice available with in each of n choice situations (referred to as items).

The function returns three large lists containing objects that can be used to assess: (1) the probability that a choice will be made, and (2) the quantity of information, called surprisal, that the choice made reveals about the performance or experience of the person making the choice.

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.

Examples

Run this code

if (FALSE) {
  #  Example 1:  Input choice data and key for the short version of the 
  #  SweSAT quantitative multiple choice test with 24 items and 1000 examinees
  #  input the choice indices in the 1000 by 24 choice index matrix
  chcemat <- Quant_13B_problem_chcemat
  #  set up the key data
  key     <- Quant_13B_problem_key
  # number of examinees and of items
  N <- nrow(chcemat)
  n <- ncol(chcemat)
  # number of options per item and option weights
  noption <- rep(0,n)
  for (i in 1:n) noption[i]  <- 4
  scoreList <- list() # option scores
  for (item in 1:n){
    scorei <- rep(0,noption[item])
    scorei[key[item]] <- 1
    scoreList[[item]] <- scorei
  }
  #  Analyze the data and return the big three list objects:
  #  dataList (input info), parmList (score index info) and
  #  infoList (information or scope info)
  TGresult <- TG_analysis(chcemat, scoreList, noption, 
                          NumBasis=4, ncycle=10, verbose=TRUE)}

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