# DFfun: Compute the first and second derivatives of the negative log... In TestGardener: Information Analysis for Test and Rating Scale Data

 DFfun R Documentation

## 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
``````

TestGardener documentation built on May 29, 2024, 3:31 a.m.