An extension of the Fisher Scoring Algorithm to combine PLS regression with GLM estimation in the multivariate context. Covariates can also be grouped in themes.

**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 CRANinstall.packages("SCGLR")# Install development version from GitHubdevtools::install_github("SCnext/SCGLR")

**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.

This major version introduces a new feature allowing to group covariates in so called **themes**.

- added
`scglrTheme`

and`scglrThemeBackward`

to handle theme oriented selection - reworked
`multivariateFormula`

to handle themes - added new plots targeting themes
- deprecated
`barplot`

in favor of`screeplot`

(same parameters)

- Removed LPLS legacy method
- changed from ING to PING

- New method is available : SR (Structural Relevance) see vignette
- Major rewrite of plot styling (not backward compatible)
- Various fixes and improvements (especially when dealing with a single dependant variable)

Initial version of SCGLR

- method LPLS (Local PLS)