WALS (version 0.2.5)

computeGamma1r: Internal function: Computes fully restricted one-step ML estimator for transformed regressors in walsNB

Description

Computes one-step ML estimator of fully restricted model (coefs of transformed regressors of \(\bar{Z}_1\)) in walsNB by using SVD on transformed design matrix of the focus regressors \(\bar{Z}_1\). The matrix \(\bar{Z_1}\) should have full column rank.

Usage

computeGamma1r(
  U,
  V,
  singularVals,
  ellStart,
  gStart,
  epsilonStart,
  qStart,
  y0Start,
  tStart,
  psiStart
)

Arguments

U

Left singular vectors of \(\bar{Z}_1\) from svd.

V

Right singular vectors of \(\bar{Z}_1\) from svd.

singularVals

Singular values of \(\bar{Z}_1\) from svd.

ellStart

Vector \(\bar{\ell}\) see details.

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 huynhwalsnb;textualWALS.

epsilonStart

Scalar \(\bar{\epsilon}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.

qStart

Vector \(\bar{q}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.

y0Start

Vector \(\bar{y}_0\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.

tStart

Scalar \(\bar{t}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.

psiStart

Diagonal matrix \(\bar{\Psi}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.

Details

See section "Simplification for computing \(\tilde{\gamma}_{1r}\)" in the appendix of huynhwals;textualWALS for details of the implementation and for the definitions of argument ellStart.

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

Uses svdLSplus under-the-hood.

References