  Here we propose an algorithm, named generalized orthogonal components
regression (GOCRE), to explore the relationship between a categorical outcome
and a set of massive variables. A set of orthogonal components are sequentially
constructed to account for the variation of the categorical outcome, and
together build up a generalized linear model (GLM). This algorithm can be
considered as an extension of the partial least squares (PLS) for GLMs, but
overcomes several issues of existing extensions based on iteratively reweighted
least squares (IRLS). First, existing extensions construct a different set of
components at each iteration and thus cannot provide a convergent set of
components. Second, existing extensions are computationally intensive because
of repetitively constructing a full set of components. Third, although they
pursue the convergence of regression coefficients, the resultant regression
coefficients may still diverge especially when building logistic regression
models. GOCRE instead sequentially builds up each orthogonal component upon
convergent construction, and simultaneously regresses against these orthogonal
components to fit the GLM. The performance of the new method is demonstrated by
both simulation studies and a real data example.

Methodology;Computation