computeX2M1X2: Internal function: Computes X2M1X2 for walsNB when SVD is...
In WALS: Weighted-Average Least Squares Model Averaging

computeX2M1X2

R Documentation

Internal function: Computes X2M1X2 for walsNB when SVD is applied to Z1

Description

Exploits the SVD of \bar{Z}_1 to compute \bar{X}_{2}^{\top} \bar{M}_{1} \bar{X}_{2} to avoid directly inverting \bar{Z}_{1}^{\top} \bar{Z}_{1}.

Usage

computeX2M1X2(
  X2,
  X2start,
  qStart,
  U,
  UellStart,
  ellStart,
  psiStart,
  gStart,
  epsilonStart,
  geB
)

Arguments

`X2`	Design matrix for auxiliary regressors
`X2start`	Transformed design matrix for auxiliary regressors. Refers to `\bar{X}_{2} = \bar{\Psi}^{1/2} X_{2}`.
`qStart`	Vector `\bar{q}`, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
`U`	`U` of SVD of `Z_1`. See details.
`UellStart`	Vector `U \bar{\ell}`, see details.
`ellStart`	Vector `\bar{\ell}` see details.
`psiStart`	Diagonal matrix `\bar{\Psi}`, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
`gStart`	Derivative of dispersion parameter `\rho` of NB2 with respect to `\alpha = \log(\rho)` evaluated at starting values of one-step ML. `gStart` is a scalar. See section "ML estimation" of \insertCitehuynhwalsnb;textualWALS.
`epsilonStart`	Scalar `\bar{\epsilon}`, see section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for definition.
`geB`	`\bar{g} \bar{\epsilon} / (1 + B)`. In code `gStart*epsilonStart / (1+B)`. See details for definition of `B`. `gStart` is `\bar{g}` and `epsilonStart` is `\bar{\epsilon}`.

Details

See section "Simplification for computing \bar{X}_{2}^{\top} \bar{M}_{1} \bar{X}_{2}" in the appendix of \insertCitehuynhwals;textualWALS for details of the implementation and for the definitions of arguments Uellstart, ellStart, and geB.

All parameters that contain "start" feature the starting values for the one-step ML estimation of submodels. See section "One-step ML estimator" of \insertCitehuynhwalsnb;textualWALS for details.