# Spca: Functional principal components analysis of information curve In TestGardener: Information Analysis for Test and Rating Scale Data

 Spca R Documentation

## 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.

`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
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))
``````

TestGardener documentation built on May 29, 2024, 3:31 a.m.