msos (version 1.2.0)

bsm.simple: Helper function to determine \(\beta\) estimates for MLE regression.

Description

Generates \(\beta\) estimates for MLE using a conditioning approach.

Usage

bsm.simple(x, y, z)

Arguments

x

An \(N \times (P + F)\) design matrix, where \(F\) is the number of columns conditioned on. This is equivalent to the multiplication of \(xyzb\).

y

The \(N \times (Q - F)\) matrix of observations, where \(F\) is the number of columns conditioned on. This is equivalent to the multiplication of \(Yz_a\).

z

A \((Q - F) \times L\) design matrix, where \(F\) is the number of columns conditioned on.

Value

A list with the following components:

Beta

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

SE

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

T

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

Cx

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

Details

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

See Also

bothsidesmodel.mle and bsm.fit

Examples

# NOT RUN {
# 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))
# }