TestGardener (version 3.3.6)

DFfun: 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)

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

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.

Author

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