Sigmatheta: Model-Implied Variance-Covariance Matrix \boldsymbol{Sigma}...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

Description Usage Arguments Details Value Author(s) See Also Examples

Model-implied variance-covariance matrix \boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right) from parameters of a k-variable linear regression model.

1	Sigmatheta(slopes, sigma2epsilon, SigmaX)

`slopes`	Numeric vector of length `p` or `p` by `1` matrix. p \times 1 column vector of regression slopes ≤ft( \boldsymbol{β}_{2, 3, \cdots, k} = ≤ft\{ β_2, β_3, \cdots, β_k \right\} \right) .
`sigma2epsilon`	Numeric. Variance of the error term \varepsilon ≤ft( σ_{\varepsilon}^{2} \right).
`SigmaX`	`p` by `p` numeric matrix. p \times p matrix of variances and covariances between regressor variables {X}_{2}, {X}_{3}, \cdots, {X}_{k} ≤ft( \boldsymbol{Σ}_{\mathbf{X}} \right).

The following are the parameters of a linear regression model for the covariance structure

\boldsymbol{β}_{2, \cdots, k} is the p \times 1 column vector of regression slopes,
σ_{\varepsilon}^{2} is the variance of the error term \varepsilon, and
\boldsymbol{Σ}_{\mathbf{X}} is the p \times p matrix of variances and covariances of {X}_{2}, {X}_{3}, \cdots, {X}_{k}.

Returns the model-implied variance-covariance matrix \boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right). Note that the first item corresponds to y. The rest of the items correspond to how SigmaX is arranged.

Ivan Jacob Agaloos Pesigan

Other model-implied functions: mutheta()

slopes <- c(0.207648, 0.451039)
sigma2epsilon <- 0.9310598
SigmaX <- matrix(
  data = c(1.2934694, 0.4379592, 0.4379592, 1.0779592),
  ncol = 2
)
Sigmatheta(slopes = slopes, sigma2epsilon = sigma2epsilon, SigmaX = SigmaX)