bsm.simple {msos}

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.

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 \beta.

SE

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

T

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

Cx

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

See Also

bothsidesmodel.mle and bsm.fit

Examples

# 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))