spaMM (version 4.5.0)

spaMM_glm.fit: Fitting generalized linear models without initial-value or divergence headaches

Description

spaMM_glm.fit is a stand-in replacement for glm.fit, which can be called through glm by using glm(<>, method="spaMM_glm.fit"). Input and output structure are exactly as for glm.fit. It uses a Levenberg-Marquardt algorithm to prevent divergence of estimates. For models families such as Gamma() (with default inverse link) where the linear predictor is constrained to be positive, if the rcdd package is installed, the function can automatically find valid starting values or else indicate that no parameter value is feasible. It also automatically provides good starting values in some cases where the base functions request them from the user (notably, for gaussian(log) with some negative response). spaMM_glm is a convenient wrapper, calling glm with default method glm.fit, then calling method spaMM_glm.fit, with possibly different initial values, if glm.fit failed.

Usage

spaMM_glm.fit(x, y, weights = rep(1, nobs), start = NULL, etastart = NULL, 
              mustart = NULL, offset = rep(0, nobs), family = gaussian(), 
              control = list(maxit=200), intercept = TRUE, singular.ok = TRUE)
spaMM_glm(formula, family = gaussian, data, weights, subset,
          na.action, start = NULL, etastart, mustart, offset,
          control = list(...), model = TRUE, method = c("glm.fit","spaMM_glm.fit"),
          x = FALSE, y = TRUE, singular.ok = TRUE, contrasts = NULL, strict=FALSE, ...)

Value

An object inheriting from class glm. See glm for details.

Arguments

All arguments except strict are common to these functions and their stats package equivalents, glm and glm.fit. Most arguments operate as for the latter functions, whose documentation is repeated below. The control argument may operate differently.

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 in the ‘Details’ section of glm.

family

a description of the error distribution and link function to be used in the model. For spaMM_glm this can be a character string naming a family function, a family function or the result of a call to a family function. For spaMM_glm.fit only the third option is supported. (See family for details of family functions.)

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm is called.

weights

an optional vector of ‘prior weights’ to be used in the fitting process. Should be NULL or a numeric vector.

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 by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

start

starting values for the parameters in the linear predictor.

etastart

starting values for the linear predictor.

mustart

starting values for the vector of means.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset.

control

a list of parameters for controlling the fitting process. This is passed to glm.control, as for glm.fit. Because one can assume that spaMM_glm.fit will converge in many cases where glm.fit does not, spaMM_glm.fit allows more iterations (200) by default. However, if spaMM_glm.fit is called through glm(. . ., method="spaMM_glm.fit"), then the number of iterations is controlled by the glm.control call within glm, so that it is 25 by default, overriding the spaMM_glm.fit default.

model

a logical value indicating whether model frame should be included as a component of the returned value.

method

A 2-elements vector specifying first the method to be used by spaMM_glm in the first attempt to fit the model, second the method to be used in a second attempt if the first failed. Possible methods include those shown in the default, "model.frame", which returns the model frame and does no fitting, or user-supplied fitting functions. These functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as glm.fit.

x, y

For spaMM_glm: x is a design matrix of dimension n * p, and y is a vector of observations of length n.

For spaMM_glm.fit: x is a design matrix of dimension n * p, and y is a vector of observations of length n.

singular.ok

logical; if FALSE a singular fit is an error.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

intercept

logical. Should an intercept be included in the null model?

strict

logical. Whether to perform a fit by spaMM_glm.fit if glm.fit returned the warning "glm.fit: algorithm did not converge".

...

arguments to be used to form the default control argument if it is not supplied directly.

Examples

x <- c(8.752,20.27,24.71,32.88,27.27,19.09)
y <- c(5254,35.92,84.14,641.8,1.21,47.2)

# glm(.) fails:
(check_error <- try(glm(y~ x,data=data.frame(x,y),family=Gamma(log)), silent=TRUE))
if ( ! inherits(check_error,"try-error")) stop("glm(.) call unexpectedly succeeded")

spaMM_glm(y~ x,data=data.frame(x,y),family=Gamma(log))

## Gamma(inverse) examples
x <- c(43.6,46.5,21.7,18.6,17.3,16.7)
y <- c(2420,708,39.6,16.7,46.7,10.8)

# glm(.) fails (can't find starting value)
(check_error <- suppressWarnings(try(glm(y~ x,data=data.frame(x,y),family=Gamma()) , silent=TRUE)))
if ( ! inherits(check_error,"try-error")) stop("glm(.) call unexpectedly succeeded.")

if (requireNamespace("rcdd",quietly=TRUE)) {
  spaMM_glm(y~ x,data=data.frame(x,y),family=Gamma())
}

## A simple exponential regression with some negative response values

set.seed(123)
x <- seq(50)
y <- exp( -0.1 * x) + rnorm(50, sd = 0.1)
glm(y~ x,data=data.frame(x,y),family=gaussian(log), method="spaMM_glm.fit")

# => without the 'method' argument, stats::gaussian(log)$initialize() is called 
# and stops on negative response values.