# bothsidesmodel.df: Obtain the degrees of freedom for a model. In msos: Data Sets and Functions Used in Multivariate Statistics: Old School by John Marden

## Description

Determines the denominators needed to calculate an unbiased estimator of Σ_R.

## Usage

 `1` ```bothsidesmodel.df(xx, n, pattern) ```

## Arguments

 `xx` Result of (X^T * X), where T denotes tranpose. `n` Number of rows in observation matrix given `pattern` An N x P matrix of 0's and 1's indicating which elements of β are allowed to be nonzero.

## Value

A `numeric` matrix of size N x N containing the degrees of freedom for the test.

`bothsidesmodel`, `bothsidesmodel.chisquare`, `bothsidesmodel.hotelling`, `bothsidesmodel.lrt`, and `bothsidesmodel.mle`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# Find the DF for a likelihood ratio test statistic. x <- cbind( 1, c(-2, -1, 0, 1, 2), c(2, -1, -2, -1, 2), c(-1, 2, 0, -2, 1), c(1, -4, 6, -4, 1) ) # or x <- cbind(1, poly(1:5, 4)) data(skulls) x <- kronecker(x, rep(1, 30)) y <- skulls[, 1:4] z <- diag(4) pattern <- rbind(c(1, 1, 1, 1), 1, 0, 0, 0) xx <- t(x) %*% x bothsidesmodel.df(xx, nrow(y), pattern) ```