etas: Eta coefficients

In mbojan/mbstats: Michal's Beautiful Selection of Totally Awesome and Trustworthy Statistical functions

Description

Calculate Eta coefficients, known as "Correlation ratios". Squared value of Eta has an interpretation in terms of the proportion of explained variance. The interpretation follows from a problem of predicting values of y. The value of the Eta^2 is the proportion by which the error of predicting values of y is reduced by using the information provided by x.

Usage

etas(object, ...)

## Default S3 method:
etas(object, fac, pop_var = FALSE, ...)

## S3 method for class 'anova'
etas(object, ...)

## S3 method for class 'lm'
etas(object, ...)

Arguments

object	the R object
...	arguments passed to other methods
fac	vector for conditioning variable
pop_var	logical, whether to use population or sample variance in the calculation

Value

Values of eta and partial eta coefficients.

Methods (by class)

• default: The default method expect vectors. The function requires additional argument fac – a vector of the same length as object. The result is a value (vector of length 1) of the Eta^2 assuming that we want to predict the values of object with the values of fac using the so called "Type I regression of means". For two variables y and x the Eta is given by the formula:

  Eta^2 = ( D^2(y) - E[D^2(y|x)] ) / D^2(y)

• anova: For objects of class anova the function calculates the Eta's and Partial Eta Squares for all effects in the given model. In this setting the eta squares for the given effect are equal to:

  SSeffect / SStotal

  where SS are appropriate Sums of Squares. The “Partial Eta Squares” for the given effect are equal to:

  SSeffect / (SSeffect+SSresid)

  The function returns a data frame with columns Eta and Partial Eta with a row for every term in the model.

• lm: For objects of class lm the function is applied on the result of calling anova().

Examples

### Generate some data
x1 <- rnorm(50)
x2 <- rnorm(50)
y <- 5 + 2 * x1 + rnorm(50, 0, 2) + 3 * x2 + rnorm(50, 0, .5)

### Method for vectors
etas(y, rep(1:2, each = 25))

### Method for 'lm' which calls 'anova'
m <- lm(y ~ x1 + x2)
etas(m)

mbojan/mbstats documentation built on Dec. 21, 2021, 3:56 p.m.