formula.GeDS {GeDS}

Formula for the predictor model

Description

A description of the structure of a predictor model to be fitted using NGeDS and/or GGeDS and how this information can be extracted from a GeDS-class object.

Usage

## S3 method for class 'GeDS'
formula(x, ...)

Arguments

x

Fitted GeDS-class object, tipically produced by NGeDS or GGeDS from which the predictor model formula should be extracted.

...

Unused in this case.

Details

In the GeDS GNM (GLM) regression, implemented in NGeDS and GGeDS, it is assumed that the mean of the response variable transformed using an appropriate link function is modelled through a possibly multivariate predictor model involving two components: a GeD variable knot spline regression component involving up to two of the independent variables and a parametric component with respect to the remaining independent variables. The formula is used to specify the structure of such a possibly multivariate predictor model.

The formulae that are input in NGeDS and GGeDS are similar to those input in lm or glm except that the function f should be specified in order to identify which of the covariates enter the GeD spline regression part of the predictor model. For example, if the predictor model is univariate and it links the transformed means of y to x1, the predictor has only a GeD spline component and the formula should be in the form y ~ f(x1).

As noted, there may be additional independent variables, x2, x3, ... which may enter linearly into the parametric component of the predictor model and not be part of the GeD spline regression component. For example one may use the formula y ~ f(x1) + x2 + x3 which assumes a spline regression only between the transformed mean of y and x1, while x2 and x3 enter the predictor model just linearly.

In the current version of the package, GGeDS is univariate, therefore only one covariate which enters the spline regression component can be specified.

In contrast, the function NGeDS, generates also bivariate GeDS regression models. Therefore, if the functional dependence of the mean of the response variable y on x1 and x2 needs to be jointly modelled and there are no other covariates, the formula for the corresponding two dimensional predictor model should be specified as y ~ f(x1,x2).

Within the argument formula, similarly as in other R functions, it is possible to specify one or more offset variables, i.e. known terms with fixed regression coefficients equal to 1. These terms should be identified via the function offset.