# Ensure that estimated score index is global Multiple minima are found quite often in the data fitting function that is minimized using function `indexfun`, and in roughly 10 percent of the estimates there is a minimum that it lower than that detected. The function searches a mesh of 101 points for minima, computes the fitting function at the minima, and assigns the location of the global minimum as the replacement index if the location differs by more than 0.5 from the value identified by `index_fun`. The function values and their first two derivatives are also replaced. ```r index_search(SfdList, chcemat, index, Fval, DFval, D2Fval, indexind=1:N) ``` ## Arguments - `SfdList`: A list vector containing specifications of surprisal curves for each item. - `chcemat`: An `N` by `n` matrix containing indices of chosen items for each test taker. - `index`: A vector containing all the score index values. - `Fval`: A vector containing the `N` function values. - `DFval`: A vector containing the `N` first derivative values. - `D2Fval`: A vector containing the `N` second derivative values. - `indexind`: A vector containing indices of values to be processed. ## Returns A named list object containing objects produced from analyzing the simulations, one set for each simulation: - **index:**: A vector containing all the score index values including those that are altered. - **Fval:**: A vector containing the N function values included those that are altered. - **DFval:**: A vector containing the N first derivative values included those that are altered. - **D2Fval:**: A vector containing the N second derivative values included those that are altered. - **changeindex:**: Indices of the index values that are altered ## 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_fun` ## Examples ```r # Search for values of index that are not at the global minimum of the # fitting function and replace them as well as their function and # derivative values associated with the fine grid value nearest the # the global minimum. chcemat <- Quant_13B_problem_chcemat key <- Quant_13B_problem_key SfdList <- Quant_13B_problem_parmList$SfdList index <- Quant_13B_problem_parmList$index Fval <- Quant_13B_problem_parmList$Fval DFval <- Quant_13B_problem_parmList$DFval D2Fval <- Quant_13B_problem_parmList$D2Fval Result <- index_search(SfdList, chcemat, index, Fval, DFval, D2Fval) changeindex <- Result$changeindex print(paste("Number changed =",length(changeindex))) change <- index[changeindex] - Result$index[changeindex] ```

index_search function