# etas: Calculate Eta coefficients In mbojan/mbtools: Chaotic Collection of Functions and Datasets Possibly Useful Also To Others

## Description

This generic function calculates Eta coefficients which are also known as “Correlation ratios” or (the squared value) as the “Proportion of explained variance”.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```etas(object, ...) ## Default S3 method: etas(object, fac, ...) ## 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

## Details

The Eta coefficient (more specifically its squared value) has a interpretation in terms of the proportion of explained variance.

In the decision theory the interpretation is related to the identification problem that involves two variables: y and x. The task is two identify the 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 contained in x.

For numeric vectors the function requires additional argument: a vector of the same length as the first. The result is a value 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)

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

SSeffect / (SSeffect+SSresid)

For objects of class `lm` the function is applied on the result of calling `anova`.

## Value

Values of eta and partial eta coefficients.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```x1 <- rnorm(50) x2 <- rnorm(50) y <- 5 + 2*x1 + rnorm(50,0,2) + 3*x2 + rnorm(50,0,.5) # method for numeric etas( y, rep(1:2, each=25) ) # method for 'lm' which calls 'anova' m <- lm( y ~ x1 + x2 ) etas(m) ```

mbojan/mbtools documentation built on Nov. 9, 2017, 3:21 p.m.