Solves the equation system in walsNB via Sherman-Morrison-Woodbury formula for the unrestricted estimator \(\hat{\gamma}_{u}\).
svdLSplus(U, V, singularVals, y, ell, geB)Left singular vectors of \(\bar{Z}\) or \(\bar{Z}_{1}\)
from svd.
Right singular vectors of \(\bar{Z}\) or \(\bar{Z}_{1}\)
from svd.
Singular values of \(\bar{Z}\) or \(\bar{Z}_{1}\)
from svd.
"Pseudo"-response, see details.
Vector \(\bar{\ell}\) from section "Simplification for computing \(\tilde{\gamma}_{u}\)" huynhwals;textualWALS
Scalar \(\bar{g} \bar{\epsilon} / (1 + B)\). See section "Simplification for computing \(\tilde{\gamma}_{u}\)" huynhwals;textualWALS for definition of \(\bar{g}\), \(\bar{\epsilon}\) and \(B\).
The function can be reused for the computation of the fully restricted estimator \(\tilde{\gamma}_{1r}\) and the model averaged estimator \(\hat{\gamma}_{1}\).
For \(\tilde{\gamma}_{1r}\) and \(\hat{\gamma}_{1}\) use
U, V and singularVals from SVD of \(\bar{Z}_{1}\).
For \(\hat{\gamma}_{u}\) and \(\tilde{\gamma}_{1r}\) use same
pseudo-response \(\bar{y_{0}} - \bar{t} \bar{\epsilon} \bar{\Psi}^{-1/2} \bar{q}\)
in argument y.
For \(\hat{\gamma}_{1}\) use pseudo-response \(\bar{y_{0}} - \bar{t} \bar{\epsilon} \bar{\Psi}^{-1/2} \bar{q} - (\bar{Z}_{2} + \bar{g} \bar{\epsilon} \bar{\Psi}^{-1/2} \bar{q} \bar{q}^{\top} Z_{2}) \hat{\gamma}_{2}\).
See section "Note on function svdLSplus from WALS" in huynhwals;textualWALS.