bothsidesmodel function

Calculate the least squares estimates

This function fits the model using least squares. It takes an optional pattern matrix P as in (6.51), which specifies which $\beta _{ij}$'s are zero.

bothsidesmodel(x, y, z = diag(qq), pattern = matrix(1, nrow = p, ncol = l))

Arguments

• x: An $N x P$ design matrix.
• y: The $N x Q$ matrix of observations.
• z: A $Q x L$ design matrix
• pattern: An optional $N x P$ matrix of 0's and 1's indicating which elements of $\beta$ are allowed to be nonzero.

Returns

A list with the following components:

• Beta: The least-squares estimate of $\beta$.
• SE: The $P x L$ matrix with the $ij$th element being the standard error of $\hat{\beta}_ij$.
• T: The $P x L$ matrix with the $ij$th element being the $t$-statistic based on $\hat{\beta}_{ij}$.
• Covbeta: The estimated covariance matrix of the $\hat{\beta}_{ij}$'s.
• df: A $p$-dimensional vector of the degrees of freedom for the $t$-statistics, where the $j$th component contains the degrees of freedom for the $j$th column of $\hat{\beta}$.
• Sigmaz: The $Q x Q$ matrix $\hat{\Sigma}_z$.
• Cx: The $Q x Q$ residual sum of squares and crossproducts matrix.

Examples

# Mouth Size Example from 6.4.1
data(mouths)
x <- cbind(1, mouths[, 5])
y <- mouths[, 1:4]
z <- cbind(c(1, 1, 1, 1), c(-3, -1, 1, 3), c(1, -1, -1, 1), c(-1, 3, -3, 1))
bothsidesmodel(x, y, z)

See Also

bothsidesmodel.chisquare, bothsidesmodel.df, bothsidesmodel.hotelling, bothsidesmodel.lrt, and bothsidesmodel.mle.