TestGardener (version 3.3.6)

Analyze: Analyze test or rating scale data defined in dataList.

Description

The test or rating scale data have already been processed by function make_dataList or other code to produce the list object dataList. The user defines a list vector ParameterList which stores results from a set of cycles of estimating surprisal curves followed by estimating optimal score index values for each examinee or respondent. These score index values are within the interval [0,100]. The number of analysis cycles is the length of the parmList list vector.

Usage

Analyze(index, indexQnt, dataList, NumDensBasis=7, norder=4, ncycle=10,  
          itdisp=FALSE, verbose=FALSE)

Value

The list vector parmList where each member is a named list object containing the results of an analysis cycle. These results are:

index:

The optimal estimates of the score index values for the examinees/respondents. This is a vector of length N.

indexQnt:

A vector of length 2*nbin+1 containing bin boundaries alternating with bin edges.

SfdList:

A list vector containing results from the estimation of surprisal curves. The list vector is of length n, the number of questions or items in the test of rating scale. For details concerning these results, see function Sbinsmth().

meanF:

For each person, the mean of the optimal fitting function values.

binctr:

A vector of length nbin containing the bin centers within the interval [0,100].

bdry:

A vector of length nbin+1 containing the bin boundaries.

freq:

A vector of length nbin containing the number of score index values in the bins. An score index value is within a bin if it is less than or equal to the upper boundary and greater than the lower boundary. The first boundary also contains zero values.

pdf_fd

Functional probability curves

logdensfd:

A functional data object defining the estimate of the log of the probability density function for the distribution of the score index values.

C:

The normalizing value for probability density functions. A density value is computed by dividing the exponential of the log density value by this constant.

denscdf:

The values over a fine mesh of the cumulative probability distribution function. These values start at 0 and end with 1 and are increasing. Ties are often found at the upper boundary, so that using these values for interpolation purposes may require using the vector unique(denscdf).

indcdf

Equally spaced index values to match the number in denscdf.

Qvec

Locations of the marker percents.

index

The positions of each test taker on the score index continuum.

Fval:

A vector of length N containing the values of the negative log likelihood fitting criterion.

DFval:

A vector of length N containing the values of the first derivative of the negative log likelihood fitting criterion.

D2Fval:

A vector of length N containing the values of the second derivative of the negative log likelihood fitting criterion.

active:

A vector of length N of the activity status of the values of index. If convergence was not achieved, the value is TRUE, otherwise FALSE.

infoSurp:

The length of the space curve defined by the surprisal curves.

Arguments

index

A vector of N score index values for the examinees or respondents. These values are in the percent interval [0,100].

indexQnt

A vector of length 2*nbin + 1 where nbin is the number of bins containing score index values. The vector begins with the lower boundary 0 and ends with the upper boundary 100. In between it alternates between the bin center value and the boundary separating the next bin.

dataList

A list that contains the objects needed to analyse the test or rating scale with the following fields:

chce:

A matrix of response data with N rows and n columns where N is the number of examinees or respondents and n is the number of items. Entries in the matrices are the indices of the options chosen. Column i of chce is expected to contain only the integers 1,...,noption.

optList:

A list vector containing the numerical score values assigned to the options for this question.

key:

If the data are from a test of the multiple choices type where the right answer is scored 1 and the wrong answers 0, this is a numeric vector of length n containing the indices the right answers. Otherwise, it is NULL.

Sfd:

An fd object for the defining the surprisal curves.

noption:

A numeric vector of length n containing the numbers of options for each item.

nbin:

The number of bins for binning the data.

scrrng:

A vector of length 2 containing the limits of observed sum scores.

scrfine:

A fine mesh of test score values for plotting.

scrvec:

A vector of length N containing the examinee or respondent sum scores.

itemvec:

A vector of length n containing the question or item sum scores.

percntrnk:

A vector length N containing the sum score percentile ranks.

indexQnt:

A numeric vector of length 2*nbin + 1 containing the bin boundaries alternating with the bin centers. These are initially defined as seq(0,100,len=2*nbin+1).

Sdim:

The total dimension of the surprisal scores.

PcntMarkers:

The marker percentages for plotting: 5, 25, 50, 75 and 95.

NumDensBasis

The number of basis functions for representing the score density.

norder

The order of the Bspline basis functions.

ncycle

The number of cycles executed by function Analyze().

itdisp

If TRUE, the progress of the iterations within each cycle for estimating index are reported.

verbose

If TRUE, the stages of analysis within each cycle for estimating index are reported.

Author

Juan Li and James Ramsay

Details

The cycling process is described in detail in the references, and displayed in R code in the vignette SweSATQuantitativeAnalysis.

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

make_dataList, TG_analysis, index_distn, index2info, index_fun, Sbinsmth

Examples

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 data as 1000 strings of length 24
  #  setup the input data list object
  dataList <- Quant_13B_problem_dataList
  #  define the initial examinee indices and bin locations
  index    <- dataList$percntrnk
  indexQnt <- dataList$indexQnt
  #  Set the number of cycles (default 10 but here 5)
  ncycle <- 5
  parmListvec <- Analyze(index, indexQnt, ncycle=ncycle, dataList, 
                         verbose=TRUE) 
  #  two column matrix containing the mean fit and arclength values
  #  for each cycle
  HALsave <- matrix(0,ncycle,2)
  for (icycle in 1:ncycle) {
    HALsave[icycle,1] <- parmListvec[[icycle]]$meanF
    HALsave[icycle,2] <- parmListvec[[icycle]]$infoSurp
  }
  #  plot the progress over the cycles of mean fit and arc length
  par(mfrow=c(2,1))
  plot(1:ncycle, HALsave[,1], type="b", lwd=2, 
       xlab="Cycle Number",ylab="Mean H")
  plot(1:ncycle, HALsave[,2], type="b", lwd=2, 
       xlab="Cycle Number", ylab="Arc Length")}