# Functional principal components analysis of information curve A test or scale analysis produces a space curve that varies with in the space of possible option curves of dimension `Sdim`. Fortunately, it is usual that most of the shape variation in the curve is within only two or three dimensions, and these can be fixed by using functional principal components analysis. ```r Spca(SfdList, nharm=2, Sdim=NULL, rotate=TRUE) ``` ## Arguments - `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. - `Sdim`: Interval over which curve is plotted. All if Sdim == NULL. - `nharm`: The number of principal components of the test information or scale curve to be used to display the curve. Must be either 2 or 3. - `rotate`: If true, rotate principal components of the test information or scale curve to be used to display the curve to VARIMAX orientation. ## Returns A named list with these members: - **harmvarmxfd**: Functional data objects for the principal components of the curve shape. - **varpropvarmx**: Proportions of variance accounted for by the principal components ## 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 `Spca_plot` ## Examples ```r # Example 1. Display the test information curve for the # short SweSAT multiple choice test with 24 items and 1000 examinees # plot a two-dimension version of manifold curve Sdim <- Quant_13B_problem_dataList$Sdim SfdList <- Quant_13B_problem_parmList$SfdList index <- Quant_13B_problem_parmList$index infoSurp <- Quant_13B_problem_parmList$infoSurp # <- Quant_13B_problem_dataList$Sdim oldpar <- par(no.readonly=TRUE) on.exit(oldpar) Results <- Spca(SfdList, nharm=2, rotate=FALSE) varprop <- Results$varpropvarmx print("Proportions of variance accounted for and their sum:") print(round(100*c(varprop,sum(varprop)),1)) # plot a three-dimension version of manifold curve SfdList <- Quant_13B_problem_parmList$SfdList index <- Quant_13B_problem_parmList$index infoSurp <- Quant_13B_problem_parmList$infoSurp Results <- Spca(SfdList, nharm=3, rotate=FALSE) varprop <- Results$varpropvarmx print("Proportions of variance accounted for and their sum:") print(round(100*c(varprop,sum(varprop)),1)) ```

Spca function