# Wpca.plot: Plot the test information or scale curve in either two or... In TestGardener: Optimal Analysis of Test and Rating Scale Data

 Wpca.plot R Documentation

## Plot the test information or scale curve in either two or three dimensions.

### Description

A test or scale analysis produces a space curve that varies with in the space of possible option curves of dimension `Wdim`. 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

```  Wpca.plot(arclength, WfdList, Wdim, nharm=2, rotate=TRUE, dodge = 1.003,
titlestr = NULL)
```

### Arguments

 `arclength` The total length of the test information or scale curve as computed by function `theta2arclen.` `WfdList` 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 `WfdList` is a named list containing information computed during the analysis. These named lists contain these objects: Wfd:A functional data object containing the `M` surprisal curves for a question. M:The number of options. Pbin:A matrix containing proportions at each bin. Wbin:A matrix containing surprisal values at each bin. Pmatfine:A matrix of probabilities over a fine mesh. Wmatfine:A matrix of surprisal values over a fine mesh. DWmatfine:A matrix of the values of the first derivative of surprisal curves over fine mesh. D2Wmatfine:A matrix of the values of the second derivative of surprisal curves over fine mesh. `Wdim` The total number of options in the test or scale. `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. `dodge` A constant greater than 1 required by ggplot2. Defaults to 1.003. `titlestr` A string for the title of the plot. Defaults to NULL.

### Value

A named list with these members:

 `pcaplot` If two dimensions or harmonics are specified, this is a `gg` or `ggplot` object that can be displayed using the `print` command. If three dimensions are specified, this is NULL. `harmvarmxfd` Functional data objects for the principal components of the curve shape. `varpropvarmx` Proportions of variance accounted for by the principal components

The principal components are VARIMAX rotated by default. The plot is displayed as a side value even if no output object is specified in the call to the function.

### 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.

http://testgardener.azurewebsites.net

### 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
WfdList    <- Quantshort_parList\$WfdList
theta      <- Quantshort_parList\$theta
arclength  <- Quantshort_parList\$arclength
Wpca.plotResults <- Wpca.plot(arclength, WfdList, Quantshort_dataList\$Wdim)
varprop <- Wpca.plotResults\$varpropvarmx
print("Proportions of variance accounted for and their sum:")
print(round(c(varprop,sum(varprop)),3))
#  plot a three-dimension version of manifold curve
WfdList    <- Quantshort_parList\$WfdList
theta      <- Quantshort_parList\$theta
arclength  <- Quantshort_parList\$arclength
Wpca.plotResults <- Wpca.plot(arclength, WfdList, Quantshort_dataList\$Wdim, nharm=3)
varprop <- Wpca.plotResults\$varpropvarmx
print("Proportions of variance accounted for and their sum:")
print(round(c(varprop,sum(varprop)),3))
#  Example 2.  Display the test information curve for the
# Symptom Distress Scale with 13 items and 473 respondents.
# Proceed as above changing "Quant" to "SDS"
```

TestGardener documentation built on June 27, 2022, 1:05 a.m.