# Construct grid of 101 values of the fitting function A fast grid of values of the fitting function or one of its first two derivatives is constructed for use in function `indexsearch`. ```r 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. ## Returns A vector of length 101 containing grid values of a derivative of the fitting function ## 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. ## Author(s) Juan Li and James Ramsay ## See Also `index_search` ## Examples ```r # 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) ```

Fcurve function