# fregre.glm: Fitting Functional Generalized Linear Models In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fregre.glm R Documentation

## Fitting Functional Generalized Linear Models

### Description

Computes functional generalized linear model between functional covariate X_j(t) (and non functional covariate Z_j) and scalar response Y using basis representation.

### Usage

```fregre.glm(
formula,
family = gaussian(),
data,
basis.x = NULL,
basis.b = NULL,
subset = NULL,
weights = NULL,
...
)
```

### Arguments

 `formula` an object of class `formula` (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under `Details`. `family` a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See `family` for details of family functions.) `data` List that containing the variables in the model. `basis.x` List of basis for functional explanatory data estimation. `basis.b` List of basis for β(t) parameter estimation. `subset` an optional vector specifying a subset of observations to be used in the fitting process. `weights` weights `...` Further arguments passed to or from other methods.

### Details

This function is an extension of the linear regression models: `fregre.lm` where the E[Y|X,Z] is related to the linear prediction η via a link function g(.).

E[Y|X,Z]= η = g^{-1}(α + ∑ β_j Z_j+∑ < X_k(t) , β_k(t) >)

where Z = [Z_1 ,..., Z_p] are the non functional covariates and X(t) = [ X_1(t_1) ,..., X_q(t_q)] are the functional ones.

The first item in the `data` list is called "df" and is a data frame with the response and non functional explanatory variables, as `glm`.

Functional covariates of class `fdata` or `fd` are introduced in the following items in the `data` list.
`basis.x` is a list of basis for represent each functional covariate. The basis object can be created by the function: `create.pc.basis`, `pca.fd` `create.pc.basis`, `create.fdata.basis` o `create.basis`.
`basis.b` is a list of basis for represent each β(t) parameter. If `basis.x` is a list of functional principal components basis (see `create.pc.basis` or `pca.fd`) the argument `basis.b` is ignored.

represent beta lower than the number of basis used to represent the functional data.

### Value

Return `glm` object plus:

• `basis.x` Basis used for `fdata` or `fd` covariates.

• `basis.b` Basis used for beta parameter estimation.

• `beta.l` List of estimated beta parameter of functional covariates.

• `data` List that containing the variables in the model.

• `formula` formula.

### Note

If the formula only contains a non functional explanatory variables (multivariate covariates), the function compute a standard `glm` procedure.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

### References

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

McCullagh and Nelder (1989), Generalized Linear Models 2nd ed. Chapman and Hall.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S, New York: Springer.

See Also as: `predict.fregre.glm` and `summary.glm`.
Alternative method if `family`=gaussian: `fregre.lm`.

### Examples

```## Not run:
data(tecator)
x=tecator\$absorp.fdata
y=tecator\$y\$Fat
tt=x[["argvals"]]
dataf=as.data.frame(tecator\$y)
nbasis.x=11
nbasis.b=7
basis1=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.x)
basis2=create.bspline.basis(rangeval=range(tt),nbasis=nbasis.b)
f=Fat~Protein+x
basis.x=list("x"=basis1)
basis.b=list("x"=basis2)
ldata=list("df"=dataf,"x"=x)
res=fregre.glm(f,family=gaussian(),data=ldata,basis.x=basis.x,
basis.b=basis.b)
summary(res)

## End(Not run)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.