Conditional Visualization for Statistical Models

Description

Exploring statistical models by interactively taking 2-D and 3-D sections in data space. The main functions for end users are ceplot (see example below) and condtour. Requires XQuartz on Mac OS, and X11 on Linux. A website for the package is available at markajoc.github.io/condvis. Source code is available to browse at GitHub. Bug reports and feature requests are very welcome at GitHub.

Details

Author(s)

Mark O'Connell <mark_ajoc@yahoo.ie>, Catherine Hurley <catherine.hurley@mu.ie>, Katarina Domijan <katarina.domijan@mu.ie>.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

Examples

## Not run: 
mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$am <- as.factor(mtcars$am)

library(mgcv)
model1 <- list(
  quadratic = lm(mpg ~ cyl + am + qsec + wt + I(wt^2), data = mtcars),
  additive = gam(mpg ~ cyl + am + qsec + s(wt), data = mtcars))

ceplot(data = mtcars, model = model1, sectionvars = "wt")

## End(Not run)

Make a list of variable pairings for condition selecting plots produced by plotxc

Description

This function arranges a number of variables in pairs, ordered by their bivariate relationships. The goal is to discover which variable pairings are most helpful in avoiding extrapolations when exploring the data space. Variable pairs with strong bivariate dependencies (not necessarily linear) are chosen first. The bivariate dependency is measured using savingby2d. Each variable appears in the output only once.

Usage

arrangeC(data, method = "default")

Arguments

Details

If data is so big as to make arrangeC very slow, a random sample of rows is used instead. The bivariate dependency measures are rough, and the ordering algorithm is a simple greedy one, so it is not worth allowing it too much time. This function exists mainly to provide a helpful default ordering/pairing for ceplot.

Value

A list containing character vectors giving variable pairings.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

savingby2d

Examples

data(powerplant)

pairings <- arrangeC(powerplant)

dev.new(height = 2, width = 2 * length(pairings))
par(mfrow = c(1, length(pairings)))

for (i in seq_along(pairings)){
 plotxc(powerplant[, pairings[[i]]], powerplant[1, pairings[[i]]],
   select.col = NA)
}

Interactive conditional expectation plot

Description

Creates an interactive conditional expectation plot, which consists of two main parts. One part is a single plot depicting a section through a fitted model surface, or conditional expectation. The other part shows small data summaries which give the current condition, which can be altered by clicking with the mouse.

Usage

ceplot(data, model, response = NULL, sectionvars = NULL,
  conditionvars = NULL, threshold = NULL, lambda = NULL,
  distance = c("euclidean", "maxnorm"), type = c("default", "separate",
  "shiny"), view3d = FALSE, Corder = "default", selectortype = "minimal",
  conf = FALSE, probs = FALSE, col = "black", pch = NULL,
  residuals = FALSE, xsplotpar = NULL, modelpar = NULL,
  xcplotpar = NULL)

Arguments

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

condtour, similarityweight

Examples

## Not run: 
## Example 1: Multivariate regression, xs one continuous predictor

mtcars$cyl <- as.factor(mtcars$cyl)

library(mgcv)
model1 <- list(
    quadratic = lm(mpg ~ cyl + hp + wt + I(wt^2), data = mtcars),
    additive = mgcv::gam(mpg ~ cyl + hp + s(wt), data = mtcars))

conditionvars1 <- list(c("cyl", "hp"))

ceplot(data = mtcars, model = model1, response = "mpg", sectionvars = "wt",
  conditionvars = conditionvars1, threshold = 0.3, conf = T)

## Example 2: Binary classification, xs one categorical predictor

mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$am <- as.factor(mtcars$am)

library(e1071)
model2 <- list(
  svm = svm(am ~ mpg + wt + cyl, data = mtcars, family = "binomial"),
  glm = glm(am ~ mpg + wt + cyl, data = mtcars, family = "binomial"))

ceplot(data = mtcars, model = model2, sectionvars = "wt", threshold = 1,
  type = "shiny")

## Example 3: Multivariate regression, xs both continuous

mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$gear <- as.factor(mtcars$gear)

library(e1071)
model3 <- list(svm(mpg ~ wt + qsec + cyl + hp + gear,
  data = mtcars, family = "binomial"))

conditionvars3 <- list(c("cyl","gear"), "hp")

ceplot(data = mtcars, model = model3, sectionvars = c("wt", "qsec"),
  threshold = 1, conditionvars = conditionvars3)

ceplot(data = mtcars, model = model3, sectionvars = c("wt", "qsec"),
    threshold = 1, type = "separate", view3d = T)

## Example 4: Multi-class classification, xs both categorical

mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$vs <- as.factor(mtcars$vs)
mtcars$am <- as.factor(mtcars$am)
mtcars$gear <- as.factor(mtcars$gear)
mtcars$carb <- as.factor(mtcars$carb)

library(e1071)
model4 <- list(svm(carb ~ ., data = mtcars, family = "binomial"))

ceplot(data = mtcars, model = model4, sectionvars = c("cyl", "gear"),
  threshold = 3)

## Example 5: Multi-class classification, xs both continuous

data(wine)
wine$Class <- as.factor(wine$Class)
library(e1071)

model5 <- list(svm(Class ~ ., data = wine, probability = TRUE))

ceplot(data = wine, model = model5, sectionvars = c("Hue", "Flavanoids"),
  threshold = 3, probs = TRUE)

ceplot(data = wine, model = model5, sectionvars = c("Hue", "Flavanoids"),
  threshold = 3, type = "separate")

ceplot(data = wine, model = model5, sectionvars = c("Hue", "Flavanoids"),
  threshold = 3, type = "separate", selectortype = "pcp")

## Example 6: Multi-class classification, xs with one categorical predictor,
##            and one continuous predictor.

mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$carb <- as.factor(mtcars$carb)

library(e1071)
model6 <- list(svm(cyl ~ carb + wt + hp, data = mtcars, family = "binomial"))

ceplot(data = mtcars, model = model6, threshold = 1, sectionvars = c("carb",
  "wt"), conditionvars = "hp")

## End(Not run)

Conditional tour; a tour through sections in data space

Description

Whereas ceplot allows the user to interactively choose sections to visualise, condtour allows the user to pre-select all sections to visualise, order them, and cycle through them one by one. ']' key advances the tour, and '[' key goes back. Can adjust threshold for the current section visualisation with ',' and '.' keys.

Usage

condtour(data, model, path, response = NULL, sectionvars = NULL,
  conditionvars = NULL, threshold = NULL, lambda = NULL,
  distance = c("euclidean", "maxnorm"), view3d = FALSE,
  Corder = "default", conf = FALSE, col = "black", pch = NULL,
  xsplotpar = NULL, modelpar = NULL, xcplotpar = NULL)

Arguments

Value

Produces a set of interactive plots. One device displays the current section. A second device shows the the current section in the space of the conditioning predictors given by conditionvars. A third device shows some simple diagnostic plots; one to show approximately how much data are visible on each section, and another to show what proportion of data are visited by the tour.

See Also

ceplot, similarityweight

Examples

## Not run: 

data(powerplant)
library(e1071)
model <- svm(PE ~ ., data = powerplant)
path <- makepath(powerplant[-5], 25)
condtour(data = powerplant, model = model, path = path$path,
  sectionvars = "AT")

data(wine)
wine$Class <- as.factor(wine$Class)
library(e1071)
model5 <- list(svm(Class ~ ., data = wine))
conditionvars1 <- setdiff(colnames(wine), c("Class", "Hue", "Flavanoids"))
path <- makepath(wine[, conditionvars1], 50)
condtour(data = wine, model = model5, path = path$path, sectionvars = c("Hue"
  , "Flavanoids"), threshold = 3)


## End(Not run)

Assign colours to numeric vector

Description

This function assigns colours on a linear scale to a numeric vector. Default is to try to use RColorBrewer for colours, and cm.colors otherwise. Can provide custom range, breaks and colours.

Usage

cont2color(x, xrange = NULL, breaks = NULL, colors = NULL)

Arguments

Details

Uses the RColorBrewer package if installed. Coerces x to numeric with a warning.

Value

A character vector of colours.

See Also

factor2color

Examples

x <- runif(200)
plot(x, col = cont2color(x, c(0,1)))

plot(x, col = cont2color(x, c(0,0.5)))

plot(sort(x), col = cont2color(sort(x), c(0.25,0.75)), pch = 16)
abline(h = c(0.25, 0.75), lty = 3)

Brockmann's crab data

Description

Abstract from original paper: Horseshoe crabs arrive on the beach in pairs and spawn in the high intertidal during the springtime, new and full moon high tides. Unattached males also come to the beach, crowd around the nesting couples and compete with attached males for fertilizations. Satellite males form large groups around some couples while ignoring others, resulting in a nonrandom distribution that cannot be explained by local environmental conditions or habitat selection. In experimental manipulations, pairs that had satellites regained them after they had been removed whereas pairs with no satellites continued nesting alone, which means that satellites were not simply accumulating around the pairs that had been on the beach the longest. Manipulations also revealed that satellites were not just copying the behaviour of other males. Based on the evidence from observations and experiments, the most likely explanation for the nonrandom distribution of satellite males among nesting pairs is that unattached males are preferentially attracted to some females over others. Females with many satellites were larger and in better condition, but did not lay more eggs, than females with few or no satellites.

satellites response variable; number of satellites around female crab
color color of crab
spine condition of spine
weight weight of crab
width width of carapace

Format

173 observations on 5 variables.

Source

https://onlinecourses.science.psu.edu/stat504/node/169

References

Brockmann, H. (1996), "Satellite male groups in horseshoe crabs," Ethology, 102-1, pp. 1-21.

Examples

data(crab)

Minkowski distance

Description

Calculate Minkowski distance between one point and a set of other points.

Usage

dist1(x, X, p = 2, inf = FALSE)

Arguments

Value

A numeric vector. These are distance^p, for speed of computation.

See Also

similarityweight

Examples

x <- runif(5000)
y <- runif(5000)

x1 <- 0.5
y1 <- 0.5

dev.new(width = 4, height = 5.3)
par(mfrow = c(2, 2))

for(p in c(0.5, 1, 2, 10)){
  d <- dist1(x = c(x1, y1), X = cbind(x, y), p = p) ^ (1/p)
  col <- rep("black", length(x))
  col[d < 0.3] <- "red"
  plot(x, y, pch = 16, col = col, asp = 1, main = paste("p = ", p, sep = ""))
}

Assign colours to factor vector

Description

This function takes a factor vector and returns suitable colours representing the factor levels. Default is to try to use RColorBrewer for colours, and rainbow otherwise. Can provide custom colours.

Usage

factor2color(x, colors = NULL)

Arguments

Details

Uses the RColorBrewer package if installed. Coerces x to factor with a warning.

Value

A character vector of colours.

See Also

cont2color

Examples

plot(iris[, c("Petal.Length", "Petal.Width")], pch = 21,
  bg = factor2color(iris$Species))
legend("topleft", legend = levels(iris$Species),
  fill = factor2color(as.factor(levels(iris$Species))))

Interpolate

Description

Interpolate a numeric or factor vector.

Usage

interpolate(x, ...)

## S3 method for class 'numeric'
interpolate(x, ninterp = 4L, ...)

## S3 method for class 'integer'
interpolate(x, ninterp = 4L, ...)

## S3 method for class 'factor'
interpolate(x, ninterp = 4L, ...)

## S3 method for class 'character'
interpolate(x, ninterp = 4L, ...)

Arguments

Make a default path for conditional tour

Description

Provides a default path (a set of sections), useful as input to a conditional tour (condtour). Clusters the data using k-means or partitioning around medoids (from the cluster package). The cluster centres/prototypes are then ordered to create a sensible way to visit each section as smoothly as possible. Ordering uses either the DendSer or TSP package. Linear interpolation is then used to create intermediate points between the path nodes.

Usage

makepath(x, ncentroids, ninterp = 4)

Arguments

Value

A list with two dataframes: centers giving the path nodes, and path giving the full interpolated path.

See Also

condtour

Examples

d <- data.frame(x = runif(500), y = runif(500))
plot(d)
mp1 <- makepath(d, 5)
points(mp1$centers, type = "b", col = "blue", pch = 16)
mp2 <- makepath(d, 40)
points(mp2$centers, type = "b", col = "red", pch = 16)

Condition selector plot

Description

Data visualisations used to select sections for ceplot.

Usage

plotxc(xc, xc.cond, name = NULL, trim = NULL, select.colour = NULL,
  select.lwd = NULL, cex.axis = NULL, cex.lab = NULL, tck = NULL,
  select.cex = 1, hist2d = NULL, fullbin = NULL, ...)

Arguments

Value

Produces a plot, and returns a list containing the relevant information to update the plot at a later stage.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

ceplot, plotxs.

plotxs, ceplot, condtour

Examples

## Histogram, highlighting the first case.

data(mtcars)
obj <- plotxc(mtcars[, "mpg"], mtcars[1, "mpg"])
obj$usr

## Barplot, highlighting 'cyl' = 6.

plotxc(as.factor(mtcars[, "cyl"]), 6, select.colour = "blue")

## Scatterplot, highlighting case 25.

plotxc(mtcars[, c("qsec", "wt")], mtcars[25, c("qsec", "wt")],
  select.colour = "blue", select.lwd = 1, lty = 3)

## Boxplot, where 'xc' contains one factor, and one numeric.

mtcars$carb <- as.factor(mtcars$carb)
plotxc(mtcars[, c("carb", "wt")], mtcars[25, c("carb", "wt")],
  select.colour = "red", select.lwd = 3)

## Spineplot, where 'xc' contains two factors.

mtcars$gear <- as.factor(mtcars$gear)
mtcars$cyl <- as.factor(mtcars$cyl)
plotxc(mtcars[, c("cyl", "gear")], mtcars[25, c("cyl", "gear")],
  select.colour = "red")

## Effect of 'trim'.

x <- c(-200, runif(400), 200)
plotxc(x, 0.5, trim = FALSE, select.colour = "red")
plotxc(x, 0.5, trim = TRUE, select.colour = "red")

Condition selector plot

Description

Multivariate data visualisations used to select sections for ceplot. Basically visualises a dataset and highlights a single point.

Usage

plotxc.pcp(Xc, Xc.cond, select.colour = NULL, select.lwd = 3,
  cex.axis = NULL, cex.lab = NULL, tck = NULL, select.cex = 1, ...)

plotxc.full(Xc, Xc.cond, select.colour = NULL, select.lwd = 3,
  cex.axis = NULL, cex.lab = NULL, tck = NULL, select.cex = 0.6, ...)

Arguments

Value

Produces a plot, and returns a list containing the relevant information to update the plot at a later stage.

See Also

ceplot, plotxs, plotxc

Visualise a section in data space

Description

Visualise a section in data space, showing fitted models where they intersect the section, and nearby observations. The weights for observations can be calculated with similarityweight. This function is mainly for use in ceplot and condtour.

Usage

plotxs(xs, y, xc.cond, model, model.colour = NULL, model.lwd = NULL,
  model.lty = NULL, model.name = NULL, yhat = NULL, mar = NULL,
  col = "black", weights = NULL, view3d = FALSE, theta3d = 45,
  phi3d = 20, xs.grid = NULL, prednew = NULL, conf = FALSE,
  probs = FALSE, pch = 1, residuals = FALSE, main = NULL, xlim = NULL,
  ylim = NULL)

Arguments

Value

A list containing relevant information for updating the plot.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

plotxc, ceplot, condtour

Examples

data(mtcars)
model <- lm(mpg ~ ., data = mtcars)
plotxs(xs = mtcars[, "wt", drop = FALSE], y = mtcars[, "mpg", drop = FALSE],
  xc.cond = mtcars[1, ], model = list(model))

Tuefekci's powerplant data

Description

The dataset contains 9568 data points collected from a Combined Cycle Power Plant over 6 years (2006-2011), when the power plant was set to work with full load. Features consist of hourly average ambient variables Temperature (T), Ambient Pressure (AP), Relative Humidity (RH) and Exhaust Vacuum (V) to predict the net hourly electrical energy output (EP) of the plant.

A combined cycle power plant (CCPP) is composed of gas turbines (GT), steam turbines (ST) and heat recovery steam generators. In a CCPP, the electricity is generated by gas and steam turbines, which are combined in one cycle, and is transferred from one turbine to another. While the Vacuum is collected from and has effect on the Steam Turbine, the other three of the ambient variables affect the GT performance.

Format

9568 observations on 5 continuous variables.

Source

UCI repository. https://archive.ics.uci.edu/ml/datasets/Combined+Cycle+Power+Plant

References

Tuefekci, P. (2014), Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods, International Journal of Electrical Power & Energy Systems, 60, pp. 126-140, ISSN 0142-0615.

Examples

data(powerplant)
head(powerplant)

Assess advantage of 2-D view over 1-D view for identifying extrapolation

Description

A simple algorithm to evaluate the advantage of by taking a bivariate marginal view of two variables, when trying to avoid extrapolations, rather than two univariate marginal views.

Usage

savingby2d(x, y = NULL, method = "default")

Arguments

Details

If given two continuous variables, the variables are both scaled to mean 0 and variance 1. Then the returned value is the ratio of the area of the convex hull of the data to the area obtained from the product of the ranges of the two areas, i.e. the area of the bounding rectangle.

If given two categorical variables, all combinations are tabulated. The returned value is the number of non-zero table entries divided by the total number of table entries.

If given one categorical and one continuous variable, the returned value is the weighted mean of the range of the continuous variable within each category divided by the overall range of the continuous variable, where the weights are given by the number of observations in each level of the categorical variable.

Requires package scagnostics if a scagnostics measure is specified in method. Requires package hdrcde if "DECR" (density estimate confidence region) is specified in method. These only apply to cases where x and y are both numeric.

Value

A number between 0 and 1. Values near 1 imply no benefit to using a 2-D view, whereas values near 0 imply that a 2-D view reveals structure hidden in the 1-D views.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

similarityweight

Examples

x <- runif(1000)
y <- runif(1000)
plot(x, y)
savingby2d(x, y)
## value near 1, no real benefit from bivariate view

x1 <- runif(1000)
y1 <- x1 + rnorm(sd = 0.3, n = 1000)
plot(x1, y1)
savingby2d(x1, y1)
## smaller value indicates that the bivariate view reveals some structure

Calculate the similarity weight for a set of observations

Description

Calculate the similarity weight for a set of observations, based on their distance from some arbitary points in data space. Observations which are very similar to the point under consideration are given weight 1, while observations which are dissimilar to the point are given weight zero.

Usage

similarityweight(x, data, threshold = NULL, distance = NULL,
  lambda = NULL)

Arguments

Details

Similarity weight is assigned to observations based on their distance from a given point. The distance is calculated as Minkowski distance between the numeric elements for the observations whose categorical elements match, with the option to use a more general dissimilarity measure comprising Minkowski distance and a mismatch count.

Value

A numeric vector or matrix, with values from 0 to 1. The similarity weights for the observations in data arranged in rows for each row in x.

References

O'Connell M, Hurley CB and Domijan K (2017). “Conditional Visualization for Statistical Models: An Introduction to the condvis Package in R.”Journal of Statistical Software, 81(5), pp. 1-20. <URL:http://dx.doi.org/10.18637/jss.v081.i05>.

See Also

dist1

Examples

## Say we want to find observations similar to the first observation.
## The first observation is identical to itself, so it gets weight 1. The
## second observation is similar, so it gets some weight. The rest are more
## different, and so get zero weight.

data(mtcars)
similarityweight(x = mtcars[1, ], data = mtcars)

## By increasing the threshold, we can find observations which are more
## approximately similar to the first row. Note that the second observation
## now has weight 1, so we lose some ability to discern how similar
## observations are by increasing the threshold.

similarityweight(x = mtcars[1, ], data = mtcars, threshold = 5)

## Can provide a number of points to 'x'. Here we see that the Mazda RX4 Wag
## is more similar to the Merc 280 than the Mazda RX4 is.

similarityweight(mtcars[1:2, ], mtcars, threshold = 3)

Italian wine data

Description

Class 3 different cultivars
Alcohol Alcohol
Malic Malic acid
Ash Ash
Alcalinity Alcalinity of ash
Magnesium Magnesium
Phenols Total phenols
Flavanoids Flavanoids
Nonflavanoid Nonflavanoid phenols
Proanthocyanins Proanthocyanins
Intensity Color intensity
Hue Hue
OD280 OD280/OD315 of diluted wines
Proline Proline

Format

178 observations on 14 variables.

Source

UCI repository. https://archive.ics.uci.edu/ml/datasets/Wine

References

S. Aeberhard, D. Coomans and O. de Vel (1992), Comparison of Classifiers in High Dimensional Settings, Technical Report 92-02, Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland.

Examples

data(wine)
pairs(wine[, -1], col = factor2color(wine$Class), cex = 0.2)