# bsm.simple: Helper function to determine beta estimates for MLE... In msos: Data Sets and Functions Used in Multivariate Statistics: Old School by John Marden

## Description

Generates β estimates for MLE using a conditioning approach.

## Usage

 1 bsm.simple(x, y, z) 

## Arguments

 x An N x (P + F) design matrix, where F is the number of columns conditioned on. This is equivalent to the multiplication of xyzb. y The N x (Q - F) matrix of observations, where F is the number of columns conditioned on. This is equivalent to the multiplication of Yz_a. z A Q-F x L design matrix, where F is the number of columns conditioned on.

## Details

The technique used to calculate the estimates is described in section 9.3.3.

## Value

A list with the following components:

Beta

The least-squares estimate of β.

SE

The (P + F) x L matrix with the ijth element being the standard error of \hat{β}_ij.

T

The (P + F) x L matrix with the ijth element being the t-statistic based on \hat{β}_ij.

Covbeta

The estimated covariance matrix of the \hat{β}_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{β}.

Sigmaz

The Q-F x Q-F matrix \hat{Σ}_z.

Cx

The Q x Q residual sum of squares and crossproducts matrix.

bothsidesmodel.mle and bsm.fit
  1 2 3 4 5 6 7 8 9 10 # Taken from section 9.3.3 to show equivalence to methods. 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)) yz <- y %*% solve(t(z)) yza <- yz[, 1:2] xyzb <- cbind(x, yz[, 3:4]) lm(yza ~ xyzb - 1) bsm.simple(xyzb, yza, diag(2))