**SCGLR** is an open source implementation of the
Supervised Component Generalized Linear Regression (Bry et al. 2013, 2016, 2018), 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
(Boulesteix and Strimmer 2007) or
ecology (Carrascal, Galván, and Gordo 2009). 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
(Tenenhaus 1998), PCA on instrumental
variables (Sabatier, Lebreton, and Chessel 1989), canonical correspondence analysis (Ter
Braak 1987), 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 (Bry and Verron 2015).

**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 (Bry et
al. 2019).

```
# Install release version from CRAN
install.packages("SCGLR")
# Install development version from GitHub
::install_github("SCnext/SCGLR") devtools
```

**SCGLR** is designed to deal with outcomes from
multiple distributions: Gaussian, Bernoulli, binomial and Poisson
separately or simultaneously (Bry et al. 2013).
Moreover **SCGLR** is also able to deal with multiple
conceptually homogeneous explanatory variable groups (Bry et al. 2018).

**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 (Chauvet, Trottier, and Bry 2018a, 2018b), or the
Cox regression model.

Boulesteix, Anne-Laure, and Korbinian Strimmer. 2007. “Partial Least
Squares: A Versatile Tool for the Analysis of High-Dimensional Genomic
Data.” *Briefings in Bioinformatics* 8 (1): 32–44. http://bib.oxfordjournals.org/content/8/1/32.short.

Bry, Xavier, Catherine Trottier, Frédéric Mortier, and Guillaume
Cornu. 2019. “Component-Based Regularisation of a Multivariate GLM with
a Thematic Partitioning of the Explanatory Variables.” *Statistical
Modelling* 19 (0): 00–00 (to appear). <https://doi.org/TO BE
ADDED>.

Bry, X., C. Trottier, F. Mortier, and G Cornu. 2018. “Component-Based
Regularisation of a Multivariate Glm with a Thematic Partitioning of the
Explanatory Variables.” *Statistical Modelling*, In press.

Bry, X., C. Trottier, F. Mortier, G. Cornu, and Verron T. 2016.
“Supervised-Component-Based Generalised Linear Regression with Multiple
Explanatory Blocks: THEME-Scglr.” In *The Multiple Facets of Partial
Least Squares and Related Methods*, edited by H. Abdi, V.E. Vinzi,
V. Russolillo, G. Saporta, and L Trinchera, 141–54. Switzerland:
Springer Proceedings in Mathematics & Statistics.

Bry, X., C. Trottier, T. Verron, and F. Mortier. 2013. “Supervised
Component Generalized Linear Regression Using a Pls-Extension of the
Fisher Scoring Algorithm.” *Journal of Multivariate Analysis*
119: 47–60. http://www.sciencedirect.com/science/article/pii/S0047259X13000407.

Bry, X., and T Verron. 2015. “THEME: THEmatic Model Exploration
Through Multiple Co-Structure Maximization.” *Journal of
Chemometrics* 29 (12): 637–47. http://onlinelibrary.wiley.com/doi/10.1002/cem.2759/full.

Carrascal, Luis M., Ismael Galván, and Oscar Gordo. 2009. “Partial
Least Squares Regression as an Alternative to Current Regression Methods
Used in Ecology.” *Oikos* 118 (5): 681–90. http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0706.2008.16881.x/full.

Chauvet, J., C. Trottier, and X Bry. 2018a. “Component-Based
Regularisation of Multivariate Generalised Linear Mixed Models.”
*Journal of Computational and Graphical Statistics*, In
press.

———. 2018b. “Regularisation of Generalised Linear Mixed Models with
Autoregressive Random Effect.” *Journal of Computational and
Graphical Statistics*, In prep.

Sabatier, R., J. D. Lebreton, and D. Chessel. 1989. “Principal
Component Analysis with Instrumental Variables as a Tool for Modelling
Composition Data.” *Multiway Data Analysis*, 341–52.

Tenenhaus, M. 1998. *La Régression PLS: Théorie et Pratique*.
Paris: Editions Technip. https://books.google.fr/books?hl=fr&lr=&id=OesjK2KZhsAC&oi=fnd&pg=PA1&dq=Tenenhaus+PLS&ots=EvUst85CEP&sig=EpksVNlZFUVoYLX7JX952PIGaHU.

Ter Braak, Cajo JF. 1987. “The Analysis of Vegetation-Environment
Relationships by Canonical Correspondence Analysis.” In *Theory and
Models in Vegetation Science*, 69–77. Springer. https://link.springer.com/chapter/10.1007/978-94-009-4061-1_7.