bsm.simple {msos}R Documentation

Helper function to determine β\beta estimates for MLE regression.

Description

Generates β\beta estimates for MLE using a conditioning approach.

Usage

bsm.simple(x, y, z)

Arguments

x

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

y

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

z

A (QF)×L(Q - F) \times L design matrix, where FF 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\beta.

SE

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

T

The (P+F)×L(P + F) \times L matrix with the ijijth element being the t-statistic based on β^ij\hat{\beta}_ij.

Covbeta

The estimated covariance matrix of the β^ij\hat{\beta}_ij's.

df

A pp-dimensional vector of the degrees of freedom for the tt-statistics, where the jjth component contains the degrees of freedom for the jjth column of β^\hat{\beta}.

Sigmaz

The (QF)×(QF)(Q - F) \times (Q - F) matrix Σ^z\hat{\Sigma}_z.

Cx

The Q×QQ \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))

[Package msos version 1.2.0 Index]