DFfun {TestGardener}

Compute the first and second derivatives of the negative log likelihoods

Description

DFfun computes the first and second derivatives of the negative log likelihoods for a set of examinees. Items can be either binary or multi-option. The analysis is within the closed interval [0,100].

Usage

  DFfun(index, SfdList, chcemat)

Arguments

index

Initial values for score indices in [0,n]/[0,100]. Vector of size N.

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.

chcemat

An N by n matrix of responses. If N = 1, it can be a vector of length n.

Value

A named list for results DF and D2F:

DF:

First derivatives of the negative log likelihood values, vector of size N

D2F:

Second derivatives of the negative log likelihood values, vector of size N

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

make_dataList, index_fun, Ffun, Ffuns_plot

Examples

  #  Example 1:
  #  Compute the first and second derivative values of the objective function  
  #  for locating each examinee for the 24-item short form of the  
  #  SweSAT quantitative test on the percentile score index continuum.
  #  Use only the first five examinees.
  chcemat <- Quant_13B_problem_dataList$chcemat
  SfdList <- Quant_13B_problem_parmList$SfdList
  index   <- Quant_13B_problem_parmList$index
  DFfunResult <- DFfun(index[1:5], SfdList, chcemat[1:5,])
  DFval  <- DFfunResult$DF
  D2Fval <- DFfunResult$D2F