Package 'multichull'

A Generic Convex-Hull-Based Model Selection Method

Description

Given a set of models for which a measure of model (mis)fit and model complexity is provided, CHull() determines the models that are located on the boundary of the convex hull and selects an optimal model by means of the scree test values.

Author(s)

Marlies Vervloet ([email protected])

References

Wilderjans, T. F., Ceulemans, E., & Meers, K. (2013). CHull: A generic convex hull based model selection method. Behavior Research Methods, 45, 1-15.

Ceulemans, E., & Kiers, H. A. L. (2006). Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method. British Journal of Mathematical & Statistical Psychology, 59, 133-150.

See Also

CHull MultiCHull

Examples

complexity.fit <- cbind(c(305,456,460,607,612,615,758,764,768,770,909,916,921,924),
c(152,89,79,71,57,57,64,49,47,47,60,41,39,39))

output <- CHull(complexity.fit)
plot(output)
print(output)
summary(output)

---

A Generic Convex-Hull-Based Model Selection Method

Description

Given a set of models for which a measure of model (mis)fit and model complexity is provided, CHull determines the models that are located on the boundary of the convex hull and selects an optimal model by means of the scree test values.

Usage

CHull(data, bound = "lower", PercentageFit = 1)

## S3 method for class 'CHull'
plot(x, col = NULL, pch = NULL, plottype = "static", ...)

## S3 method for class 'CHull'
print(x, ...)

## S3 method for class 'CHull'
summary(object, ...)

Arguments

data	Dataframe with complexity in 1st column and fit measures in 2nd column
bound	Boundary of convex hull to inspect: upper or lower
PercentageFit	Required proportion of increase in fit of a more complex model
x	An object of the type produced by CHull
col	Vector of colors used for plots
pch	Symbol used to indicate selected model(s)
plottype	Type of plot. Either 'interactive' or 'static'
...	Additional arguments
object	An object of the type produced by CHull

Value

Solution	Dataframe with selected models
Hull	Dataframe with all models on hull boundary and their st value
Origdata	Original dataframe
Bound	Boundary of convex hull that was requested
PercentageFit	Requested proportion of increase in fit of a more complex model

Details

The CHull method (Wilderjans, Ceulemans, & Meers, 2013) can be used for selecting a model by comparing model complexities (1st column of the input parameter data) and fit values (2nd column).

In a first step, only the best model (or one of the best, if some models have an equal fit) is retained per complexity. This should be a model with a high fit value if the fit measure indicates goodness-of-fit (bound="upper") and a low fit value if it indicates badness-of-fit (bound="upper"). A warning will be generated if the sign of the correlation between complexity and fit is counterintuitive in this regard.

In a second step, the remaining models are ordered (increasingly) on the basis of their complexity value.

In Step 3, models are excluded that have a higher complexity but a worse (or equal) fit when compared to the other models. This procedure is repeated until a monotonical increase (bound="upper") or decrease (bound="lower") is reached. If less than 3 models remain, the method generates the error warning that not enough data points are available for computing the convex hull and the procedure stops.

In Step 4, it is determined which models lie on the upper or lower boundary of the convex hull. Models are discarded if the improvement in fit, compared to a less complex model, is less than PercentageFit (default: PercentageFit=.01 ). The remaining models are returned in Hull.

Step 5 consists of computing the scree test values (st) for each remaining model. This is, however, not possible for the most simple and most complex model, and those models will therefore never be selected as the optimal solution, except when these are the only models that remain after the previous step.

In Step 6, the model with highest scree test value is selected, and finally, in Step 7, also models are selected that were excluded in the first step, but that have the same complexity and fit value as the selected model. All selected models end up in Solution.

References

Wilderjans, T. F., Ceulemans, E., & Meers, K. (2013). CHull: A generic convex hull based model selection method. Behavior Research Methods, 45, 1-15.

Ceulemans, E., & Kiers, H. A. L. (2006). Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method. British Journal of Mathematical & Statistical Psychology, 59, 133-150.

Examples

complexity.fit <- cbind(c(305,456,460,607,612,615,758,764,768,770,909,916,921,924),
c(152,89,79,71,57,57,64,49,47,47,60,41,39,39))

output <- CHull(complexity.fit)
plot(output)
print(output)
summary(output)

---

Reduced k-means on iris data

Description

Reduced k-means on iris data

Usage

data(chulldata)

Format

An object of class data.frame with 14 rows and 2 columns.

Examples

data(chulldata)

---

Reduced k-means on bootstrapped iris data

Description

Reduced k-means on bootstrapped iris data

Usage

data(chulldataboot)

Format

An object of class data.frame with 14 rows and 101 columns.

Examples

data(chulldataboot)

---

Convex-Hull-Based Model Selection for multiple Samples

Description

Applying the CHull function on multiple samples of fit values at once, such as bootstrap samples.

Usage

MultiCHull(data, bound = "lower", PercentageFit = 1, type = "multifit")

## S3 method for class 'MultiCHull'
plot(
  x,
  col = NULL,
  pch = NULL,
  whichticks = NULL,
  las = 2,
  plottype = "static",
  ...
)

## S3 method for class 'MultiCHullcom'
plot(x, browser = FALSE, ...)

## S3 method for class 'MultiCHull'
print(x, ...)

## S3 method for class 'MultiCHull'
summary(object, ...)

## S3 method for class 'MultiCHullcom'
summary(object, ...)

Arguments

data	Dataframe with complexity in 1st column and fit measures in next columns
bound	Boundary of convex hull to inspect: upper or lower
PercentageFit	Required proportion of increase in fit of a more complex model
type	Either 'multifit' or 'multicom'
x	object of class MultiCHullcom produced by MultiCHull
col	Vector of colors used for plots
pch	Vector of pch symbols
whichticks	Model names of ticks that should be displayed
las	Orientation of tick mark labels
plottype	Type of plot. Either 'interactive' or 'static'
...	Additional arguments
browser	If FALSE plots are viewed in viewer panel. If TRUE, plots are viewed in a browser
object	An object of the type produced by MultiCHull

Value

st	Dataframe with scree test values
tab	Table which indicates the selected model in each sample
frq	Table which indicates how often each model is selected
Origdata	Original dataframe
Bound	Boundary of convex hull that was requested
PercentageFit	Requested proportion of increase in fit of a more complex model

Details

MultiCHull function

MultiCHull applies the CHull code on multiple samples of fit values. To this end, the input parameter data consists of a dataframe with complexity values in the first column and fit values in the next columns. The different samples can for example be bootstrap samples, or fit values obtained with different random starts, or from different fit measures, etc. It is possible that in some samples no optimal solution can be found. This will generate a warning, which will include the sample number.

Data frame st contains per sample the scree test values of the solutions that were found on the upper or lower bound of the hull (see also CHull). In each sample, the least and most complex model receive a 0 value. The other models have an NA value. tab is also a dataframe, which indicates per sample the top three of optimal models (indicated by a 1, 2 and 3). The other models have an NA value. Finally, in frq the frequencies are shown for each model of being selected as the optimal model.

Plot function

Applying the method plot() on output of MultiCHull yields a plot with the models on the x-axis, ordered by increasing complexity. By default, all model names are shown as perpendicular labels on the x-axis, but one can choose to display specific model names only (e.g., whichticks=c("model13","model20")). The tick mark labels can be made horizontal, by putting parameter las to 0.

Solid lines (only shown in case of 20 or less samples) indicate the scree test values per sample, and symbols indicate the top three of the models per sample. The symbols can be adjusted with the parameter pch and the colors with col. The model (or multiple models) that is selected most often across samples, is indicated with a horizontal line.

See Also

CHull

Examples

data <- data.frame("comp"= c(305,456,460,607,612,615,758,764,768,770,909,916,921,924),
"fit"= c(152,89,79,71,57,57,64,49,47,47,60,41,39,39))
test <- array(rnorm(14*20,sd=2.5),c(14,20))
for (i in 1:20){
 data <- cbind(data, 'fit' = data[,2]+test[,i])
}
output <- MultiCHull(data)
summary(output)
plot(output)

---

Run Shiny App "multichull"

Description

Open the graphical user-interface for applying the (multi)CHull procedure

Usage

runShinyApp()

---