# fac.meanop: computes the projection matrix that produces means In dae: Functions Useful in the Design and ANOVA of Experiments

## Description

Computes the symmetric projection matrix that produces the means corresponding to a (generalized) `factor`.

## Usage

 `1` ```fac.meanop(factor) ```

## Arguments

 `factor` The (generalized) `factor` whose means the projection matrix computes from an observation-length vector.

## Details

The design matrix X for a (generalized) `factor` is formed with a column for each `level` of the (generalized) `factor`, this column being its indicator variable. The projection matrix is formed as `X %*% (1/diag(r) %*% t(X)`, where `r` is the `vector` of `levels` replications.

A generalized `factor` is a `factor` formed from the combinations of the `levels` of several original `factors`. Generalized `factors` can be formed using `fac.combine`.

## Value

A `projector` containing the symmetric, projection matrix and its degrees of freedom.

## Author(s)

Chris Brien

`fac.combine`, `projector`, `degfree`, `correct.degfree`, `fac.sumop` in package dae.
`projector` for further information about this class.
 ```1 2 3 4 5 6 7 8 9``` ```## set up a two-level factor and a three-level factor, both of length 12 A <- factor(rep(1:2, each=6)) B <- factor(rep(1:3, each=2, times=2)) ## create a generalized factor whose levels are the combinations of A and B AB <- fac.combine(list(A,B)) ## obtain the operator that computes the AB means from a vector of length 12 M.AB <- fac.meanop(AB) ```