Model-Implied Mean Vector \(\boldsymbol{\mu} \left( \boldsymbol{\theta} \right)\)

Model-implied mean vector \(\boldsymbol{\mu} \left( \boldsymbol{\theta} \right)\) from parameters of a \(k\)-variable linear regression model.

mutheta(beta, muX)

Arguments

beta	Numeric vector of length k or k by 1 matrix. \(k \times 1\) vector of regression coefficients \(\left( \boldsymbol{\beta} \right)\).
muX	Numeric vector of length p or p by 1 matrix. \(p \times 1\) column vector of means of the regressors \({X}_{2}, {X}_{3}, \cdots, {X}_{k}\) \(\left( \boldsymbol{\mu}_{\mathbf{X}} \right)\) .

Value

Returns the model-implied mean vector \(\boldsymbol{\mu} \left( \boldsymbol{\theta} \right)\). Note that the first item corresponds to the expected value of y. The rest of the items correspond to muX.

Details

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

• \(\boldsymbol{\beta}\) is the \(k \times 1\) column vector of regression coefficients, and

• \(\boldsymbol{\mu}_{\mathbf{X}}\) is the \(p \times 1\) column vector of means of the regressors \({X}_{2}, {X}_{3}, \cdots, {X}_{k}\) .

See also

Other model-implied functions: Sigmatheta()

Author

Ivan Jacob Agaloos Pesigan

Examples

beta <- c(-12.7128845, 0.2076475, 0.4510391)
muX <- c(70.18, 3.06)
mutheta(beta = beta, muX = muX)
#>           [,1]
#> [1,]  3.239997
#> [2,] 70.180000
#> [3,]  3.060000