msos (version 1.2.0)

bothsidesmodel.mle: Calculate the maximum likelihood estimates

Description

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

Usage

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

Arguments

x

An \(N \times P\) design matrix.

y

The \(N \times Q\) matrix of observations.

z

A \(Q \times L\) design matrix

pattern

An optional \(N \times P\) matrix of 0's and 1's indicating which elements of \(\beta\) are allowed to be nonzero.

Value

A list with the following components:

Beta

The least-squares estimate of \(\beta\).

SE

The \(P \times L\) matrix with the \(ij\)th element being the standard error of \(\hat{\beta}_{ij}\).

T

The \(P \times L\) 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 \(Q \times Q\) matrix \(\hat{\Sigma}_z\).

Cx

The \(Q \times Q\) residual sum of squares and crossproducts matrix.

ResidSS

The dimension of the model, counting the nonzero \(\beta _{ij}\)'s and components of \(\Sigma _z\).

Deviance

Mallow's \(C_p\) Statistic.

Dim

The dimension of the model, counting the nonzero \(\beta _{ij}\)'s and components of \(\Sigma_z\)

AICc

The corrected AIC criterion from (9.87) and (aic19)

BIC

The BIC criterion from (9.56).

See Also

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

Examples

# NOT RUN {
data(mouths)
x <- cbind(1, mouths[, 5])
y <- mouths[, 1:4]
z <- cbind(1, c(-3, -1, 1, 3), c(-1, 1, 1, -1), c(-1, 3, -3, 1))
bothsidesmodel.mle(x, y, z, cbind(c(1, 1), 1, 0, 0))
# }