Exploits the SVD of \(\bar{Z}_1\) to compute \(\bar{X}_{2}^{\top} \bar{M}_{1} \bar{X}_{2}\) to avoid directly inverting \(\bar{Z}_{1}^{\top} \bar{Z}_{1}\).
computeX2M1X2(
X2,
X2start,
qStart,
U,
UellStart,
ellStart,
psiStart,
gStart,
epsilonStart,
geB
)Design matrix for auxiliary regressors
Transformed design matrix for auxiliary regressors. Refers to \(\bar{X}_{2} = \bar{\Psi}^{1/2} X_{2}\).
Vector \(\bar{q}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
\(U\) of SVD of \(Z_1\). See details.
Vector \(U \bar{\ell}\), see details.
Vector \(\bar{\ell}\) see details.
Diagonal matrix \(\bar{\Psi}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
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.
Scalar \(\bar{\epsilon}\), see section "One-step ML estimator" of huynhwalsnb;textualWALS for definition.
\(\bar{g} \bar{\epsilon} / (1 + B)\). In code
gStart*epsilonStart / (1+B). See details for definition of \(B\).
gStart is \(\bar{g}\) and epsilonStart is \(\bar{\epsilon}\).
See section
"Simplification for computing \(\bar{X}_{2}^{\top} \bar{M}_{1} \bar{X}_{2}\)"
in the appendix of huynhwals;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 huynhwalsnb;textualWALS for details.