fwdglm: Forward Search in Generalized Linear Models
In forward: Robust Analysis using Forward Search

fwdglm

R Documentation

Forward Search in Generalized Linear Models

Description

This function applies the forward search approach to robust analysis in generalized linear models.

Usage

fwdglm(formula, family, data, weights, na.action, contrasts = NULL, bsb = NULL, 
       balanced = TRUE, maxit = 50, epsilon = 1e-06, nsamp = 100, trace = TRUE)

Arguments

`formula`	a symbolic description of the model to be fit. The details of the model are the same as for glm.
`family`	a description of the error distribution and link function to be used in the model. See `family` for details.
`data`	an optional data frame containing the variables in the model. By default the variables are taken from the environment from which the function is called.
`weights`	an optional vector of weights to be used in the fitting process.
`na.action`	a function which indicates what should happen when the data contain `NA`'s. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The default is `na.omit`.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`bsb`	an optional vector specifying a starting subset of observations to be used in the forward search. By default the `"best"` starting subset is chosen using the function `lmsglm` with control arguments provided by `nsamp`.
`balanced`	logical, for a binary response if `TRUE` the proportion of successes on the full dataset is approximately balanced during the forward search algorithm.
`maxit`	integer giving the maximal number of IWLS iterations. See `glm.control` for details.
`epsilon`	positive convergence tolerance epsilon. See `glm.control` for details.
`nsamp`	the initial subset for the forward search in generalized linear models is found by the function `lmsglm`. This argument allows to control how many subsets are used in the robust fitting procedure. The choices are: the number of samples (100 by the default) or `"all"`. Note that the algorithm tries to find `nsamp` good subsets or a maximum of 2*`nsamp` subsets.
`trace`	logical, if `TRUE` a message is printed for every ten iterations completed during the forward search.

Value

The function returns an object of class "fwdglm" with the following components:

`call`	the matched call.
`Residuals`	a `(n x (n-p+1))` matrix of residuals.
`Unit`	a matrix of units added (to a maximum of 5 units) at each step.
`included`	a list with each element containing a vector of units included at each step of the forward search.
`Coefficients`	a `((n-p+1) x p)` matrix of coefficients.
`tStatistics`	a `((n-p+1) x p)` matrix of t statistics for the coefficients, i.e. coef.est/SE(coef.est).
`Leverage`	a `(n x (n-p+1))` matrix of leverage values.
`MaxRes`	a `((n-p) x 2)` matrix of max deviance residuals in the best subsets and `m`-th deviance residuals.
`MinDelRes`	a `((n-p-1) x 2)` matrix of minimum deviance residuals out of best subsets and `(m+1)`-th deviance residuals.
`ScoreTest`	a `((n-p) x 1)` matrix of score test statistics for a goodness of link test.
`Likelihood`	a `((n-p) x 4)` matrix with columns containing: deviance, residual deviance, psuedo `R^2` (computed as `1-deviance/null.deviance`), dispersion parameter (computed as `\sum(pearson.residuals^2)/(m - p)`).
`CookDist`	a `((n-p) x 1)` matrix of forward Cook's distances.
`ModCookDist`	a `((n-p) x 5)` matrix of forward modified Cook's distances for the units (to a maximum of 5 units) included at each step.
`Weights`	a `(n x (n-p))` matrix of weights used at each step of the forward search.
`inibsb`	a vector giving the best starting subset chosen by `lmsglm`.
`binary.response`	logical, equal to `TRUE` if binary response.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

Examples

 
data(cellular)
cellular$TNF <- as.factor(cellular$TNF)
cellular$IFN <- as.factor(cellular$IFN)
mod <- fwdglm(y ~ TNF + IFN, data=cellular, family=poisson(log), nsamp=200)
summary(mod)
## Not run: plot(mod)
plot(mod, 1)
plot(mod, 5)
plot(mod, 6, ylim=c(-3, 20))
plot(mod, 7)
plot(mod, 8)

forward documentation built on Sept. 27, 2024, 5:09 p.m.