# Fcurve: Construct grid of 101 values of the fitting function In TestGardener: Information Analysis for Test and Rating Scale Data

 Fcurve R Documentation

## Construct grid of 101 values of the fitting function

### Description

A fast grid of values of the fitting function or one of its first two derivatives is constructed for use in function `indexsearch`.

### Usage

``````  Fcurve(SfdList, chcevec, nderiv=0)
``````

### Arguments

 `SfdList` A list vector containing specifications of surprisal curves for each item. `chcevec` A N by n matrix containing indices of chosen items for each test taker. `nderiv` Integer 0, 1 or 2 to indicate which level of derivative to use.

### Value

A vector of length 101 containing grid values of a derivative of the fitting function

### 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.

`index_search`

### Examples

``````#  Compute a grid of values of the objective function for locating each
#  examinee or respondent for the 24-item short form of the SweSAT
#  quantitative test on the percentile score index continuum [0,100].
chcemat <- Quant_13B_problem_dataList\$chcemat
SfdList <- Quant_13B_problem_parmList\$SfdList
index   <- Quant_13B_problem_parmList\$index
n       <- ncol(chcemat)
#  Fitting function for the first examinee
j <- 1
chcevec   <- as.numeric(chcemat[j,])
Fcurve1   <- Fcurve(SfdList, chcevec, 0)
#  First derivative of the fitting function for the first examinee
DFcurve1  <- Fcurve(SfdList, chcevec, 1)
#  Second derivative of the fitting function for the first examinee
D2Fcurve1 <- Fcurve(SfdList, chcevec, 2)
par(mfrow=c(3,1))
indfine <- seq(0,100,len=101)
plot(indfine, Fcurve1,   type="l", xlab="", ylab="Fitting curve",
main="Examinee 1")
plot(indfine, DFcurve1,  type="l", xlab="", ylab="First derivative")
points(index[1], 0, pch="o")
abline(0,0,lty=2)
plot(indfine, D2Fcurve1, type="l",
xlab="Score index", ylab="Second derivative")
abline(0,0,lty=2)
points(index[1], 0, pch="o")
par(oldpar)
``````

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