Fcurve {TestGardener}

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.

See Also

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)
oldpar  <- par(no.readonly=TRUE)
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)