savingby2d: Calculate the reduction in predictor space implied by using a 2-d marginal view rather than two 1-d views.

Description

A simple algorithm to evaluate the proportion of the predictor space which is seen to contain data by taking a bivariate marginal view of x and y, rather than two univariate marginal views.

Usage

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

Arguments

a numeric vector or factor. Can also be a dataframe containing x and y.

a numeric vector or factor.

method

criterion used to quantify bivariate relationships. Can be "default", a scagnostic measure, or "DECR" to use a density estimate confidence region.

Value

A number between 0 and 1.

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 smallest square containing the data. 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.

Examples

Run this code

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