bothsidesmodel.mle {msos}

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 ijth element being the standard error of \hat{\beta}_{ij}.

T

The P \times L matrix with the ijth 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 jth component contains the degrees of freedom for the jth 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

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))