# effects: Effects from Fitted Model

## Description

Returns (orthogonal) effects from a fitted model, usually a linear model. This is a generic function, but currently only has a methods for objects inheriting from classes `"lm"` and `"glm"`.

## Usage

 ```1 2 3 4``` ```effects(object, ...) ## S3 method for class 'lm' effects(object, set.sign = FALSE, ...) ```

## Arguments

 `object` an R object; typically, the result of a model fitting function such as `lm`. `set.sign` logical. If `TRUE`, the sign of the effects corresponding to coefficients in the model will be set to agree with the signs of the corresponding coefficients, otherwise the sign is arbitrary. `...` arguments passed to or from other methods.

## Details

For a linear model fitted by `lm` or `aov`, the effects are the uncorrelated single-degree-of-freedom values obtained by projecting the data onto the successive orthogonal subspaces generated by the QR decomposition during the fitting process. The first r (the rank of the model) are associated with coefficients and the remainder span the space of residuals (but are not associated with particular residuals).

Empty models do not have effects.

## Value

A (named) numeric vector of the same length as `residuals`, or a matrix if there were multiple responses in the fitted model, in either case of class `"coef"`.

The first r rows are labelled by the corresponding coefficients, and the remaining rows are unlabelled. Note that in rank-deficient models the corresponding coefficients will be in a different order if pivoting occurred.

## References

Chambers, J. M. and Hastie, T. J. (1992) Statistical Models in S. Wadsworth & Brooks/Cole.

`coef`
 ```1 2 3 4 5``` ```y <- c(1:3, 7, 5) x <- c(1:3, 6:7) ( ee <- effects(lm(y ~ x)) ) c( round(ee - effects(lm(y+10 ~ I(x-3.8))), 3) ) # just the first is different ```