Spca {TestGardener}

Functional principal components analysis of information curve

Description

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.

Usage

  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.

Value

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

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

Spca_plot

Examples

#  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))