scglr: Function that fits the scglr model
In SCGLR: Supervised Component Generalized Linear Regression

Description Usage Arguments Value References Examples

Calculates the components to predict all the dependent variables.

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scglr(formula, data, family, K = 1, size = NULL, weights = NULL,
  offset = NULL, subset = NULL, na.action = na.omit, crit = list(),
  method = methodSR())

`formula`	an object of class `MultivariateFormula` (or one that can be coerced to that class): a symbolic description of the model to be fitted.
`data`	a data frame to be modeled.
`family`	a vector of character of the same length as the number of dependent variables: "bernoulli", "binomial", "poisson" or "gaussian" is allowed.
`K`	number of components, default is one.
`size`	describes the number of trials for the binomial dependent variables. A (number of statistical units * number of binomial dependent variables) matrix is expected.
`weights`	weights on individuals (not available for now)
`offset`	used for the poisson dependent variables. A vector or a matrix of size: number of observations * number of Poisson dependent variables is expected.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`na.action`	a function which indicates what should happen when the data contain NAs. The default is set to `na.omit`.
`crit`	a list of two elements : maxit and tol, describing respectively the maximum number of iterations and the tolerance convergence criterion for the Fisher scoring algorithm. Default is set to 50 and 10e-6 respectively.
`method`	structural relevance criterion. Object of class "method.SCGLR" built by `methodSR` for Structural Relevance.

an object of the SCGLR class.

The function summary (i.e., summary.SCGLR) can be used to obtain or print a summary of the results.

The generic accessor functions coef can be used to extract various useful features of the value returned by scglr.

An object of class "SCGLR" is a list containing following components:

`u`	matrix of size (number of regressors * number of components), contains the component-loadings, i.e. the coefficients of the regressors in the linear combination giving each component.
`comp`	matrix of size (number of statistical units * number of components) having the components as column vectors.
`compr`	matrix of size (number of statistical units * number of components) having the standardized components as column vectors.
`gamma`	list of length number of dependant variables. Each element is a matrix of coefficients, standard errors, z-values and p-values.
`beta`	matrix of size (number of regressors + 1 (intercept) * number of dependent variables), contains the coefficients of the regression on the original regressors X.
`lin.pred`	data.frame of size (number of statistical units * number of dependent variables), the fitted linear predictor.
`xFactors`	data.frame containing the nominal regressors.
`xNumeric`	data.frame containing the quantitative regressors.
`inertia`	matrix of size (number of components * 2), contains the percentage and cumulative percentage of the overall regressors' variance, captured by each component.
`logLik`	vector of length (number of dependent variables), gives the likelihood of the model of each y_k's GLM on the components.
`deviance.null`	vector of length (number of dependent variables), gives the deviance of the null model of each y_k's GLM on the components.
`deviance.residual`	vector of length (number of dependent variables), gives the deviance of the model of each y_k's GLM on the components.

Bry X., Trottier C., Verron T. and Mortier F. (2013) Supervised Component Generalized Linear Regression using a PLS-extension of the Fisher scoring algorithm. Journal of Multivariate Analysis, 119, 47-60.

## Not run: 
library(SCGLR)

# load sample data
data(genus)

# get variable names from dataset
n <- names(genus)
ny <- n[grep("^gen",n)]    # Y <- names that begins with "gen"
nx <- n[-grep("^gen",n)]   # X <- remaining names

# remove "geology" and "surface" from nx
# as surface is offset and we want to use geology as additional covariate
nx <-nx[!nx%in%c("geology","surface")]

# build multivariate formula
# we also add "lat*lon" as computed covariate
form <- multivariateFormula(ny,c(nx,"I(lat*lon)"),A=c("geology"))

# define family
fam <- rep("poisson",length(ny))

genus.scglr <- scglr(formula=form,data = genus,family=fam, K=4,
 offset=genus$surface)

summary(genus.scglr)

## End(Not run)