In SCnext/SCGLR: Supervised Component Generalized Linear Regression

SCGLR

Introduction

SCGLR is an open source implementation of the Supervised Component Generalized Linear Regression [@bry13;-@bry16;-@bry18], which identifies, among a large set of potentially multicolinear predictors, the strong dimensions most predictive of a set of responses.

SCGLR is an extension of partial least square regression (PLSR) to the uni- and multivariate generalized linear framework. PLSR is particularly well suited for analyzing a large array of explanatory variables and many studies have demonstrated its predictive performance in various biological fields such as genetics [@boulesteix07] or ecology [@carrascal09]. While PLSR is well adapted for continuous variables, maximizing the covariance between linear combination of dependent variables, and linear combinations of covariates, SCGLR is suited for non-Gaussian outcomes and non-continuous covariates.

SCGLR is a model-based approach that extends PLS [@tenenhaus98], PCA on instrumental variables [@sabatier89], canonical correspondence analysis [@terbraak87], and other related empirical methods, by capturing the trade-off between goodness-of-fit and common structural relevance of explanatory components. The notion of structural relevance has been introduced [@bry15].

SCGLR can deal with covariates partitioned in several groups called "themes", plus a group of additional covariates. Each theme is searched for orthogonal components representing its variables in the model, whereas the additional covariates appear directly in the model, without the mediation of a component [@bry18].

SCGLR works also for mixed models using an extension of the Schall's algorithm to combine Supervised-Component regression with GLMM estimation in the multivariate context.

Installation

# Install release version from CRAN
install.packages("SCGLR")

# Install development version from GitHub
remotes::install_github("SCnext/SCGLR")

Main functions and works in progress

SCGLR is designed to deal with outcomes from multiple distributions: Gaussian, Bernoulli, binomial and Poisson separately or simultaneously [@bry13]. Moreover SCGLR is also able to deal with multiple conceptually homogeneous explanatory variable groups [@bry18].

SCGLR is a set of R functions illustrated on a floristic data set, genus. scglr and scglrTheme are respectively dedicated to fitting the model with one or more thematic group of regressors. scglrCrossVal and scglrThemeBackward are respectively dedicated to selecting the number of components. print, summary and plot methods are also available for the scglr and scglrTheme function results.

Different works are in progress both dealing for instance with the inclusion of random effects extending SCGLR to the generalized linear mixed model framework [@chauvet18;-@chauvet18b], or the Cox regression model.