glm.
gpuGlm is used to fit generalized linear models, specified by
giving a symbolic description of the linear predictor and a
description of the error distribution. Note: The QR decomposition employed by gpuLm is optimized for speed
and uses minimal pivoting.
gpuGlm(formula, family = gaussian, data, weights, subset,
na.action, start = NULL, etastart, mustart, offset, useSingle = TRUE,
control = gpuGlm.control(useSingle, ...), model = TRUE,
method = "gpuGlm.fit", x = FALSE, y = TRUE, contrasts = NULL, ...)
gpuGlm.fit(x, y, weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), family = gaussian(), useSingle,
control = gpuGlm.control(useSingle), intercept = TRUE)"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 for details of
family functions.)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.NULL or a numeric vector.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.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.glm.control
for details."gpuGlm.fit" uses iteratively reweighted
least squares (IWLS). The only current alternative is
"model.frame" which returns the model frame and does no fitting.gpuGlm:
logical values indicating whether the response vector and model
matrix used in the fitting process should be returned as components
of the returned value. For gpuGlm.fit: x is a design matrix of dimension n
* p, and y is a vector of observations of length n.
contrasts.arg
of model.matrix.default.gpuGlm: arguments to be passed by default to
glm.control: see argument control.
For weights:
further arguments passed to or from other methods.
gpuGlm returns an object of class inheriting from "glm"
which inherits from the class "lm". See later in this section.The function summary (i.e., summary.glm) can
be used to obtain or print a summary of the results and the function
anova (i.e., anova.glm)
to produce an analysis of variance table.The generic accessor functions coefficients,
effects, fitted.values and residuals can be used to
extract various useful features of the value returned by glm.weights extracts a vector of weights, one for each case in the
fit (after subsetting and na.action).An object of class "glm" is a list containing at least the
following components:In addition, non-empty fits will have components qr, R
and effects relating to the final weighted linear fit.Objects of class "glm" are normally of class c("glm",
"lm"), that is inherit from class "lm", and well-designed
methods for class "lm" will be applied to the weighted linear
model at the final iteration of IWLS. However, care is needed, as
extractor functions for class "glm" such as
residuals and weights do not just pick out
the component of the fit with the same name.If a binomial glm model was specified by giving a
two-column response, the weights returned by prior.weights are
the total numbers of cases (factored by the supplied case weights) and
the component y of the result is the proportion of successes.
response ~ terms where
response is the (numeric) response vector and terms is a
series of terms which specifies a linear predictor for
response. For binomial and quasibinomial
families the response can also be specified as a factor
(when the first level denotes failure and all others success) or as a
two-column matrix with the columns giving the numbers of successes and
failures. A terms specification of the form first + second
indicates all the terms in first together with all the terms in
second with any duplicates removed. A specification of the form first:second indicates the the set
of terms obtained by taking the interactions of all terms in
first with all terms in second. The specification
first*second indicates the cross of first and
second. This is the same as first + second +
first:second.
The terms in the formula will be re-ordered so that main effects come
first, followed by the interactions, all second-order, all third-order
and so on: to avoid this pass a terms object as the formula.
Non-NULL weights can be used to indicate that different
observations have different dispersions (with the values in
weights being inversely proportional to the dispersions); or
equivalently, when the elements of weights are positive
integers $w_i$, that each response $y_i$ is the mean of
$w_i$ unit-weight observations. For a binomial GLM prior weights
are used to give the number of trials when the response is the
proportion of successes: they would rarely be used for a Poisson GLM.
gpuGlm.fit is the workhorse function: it is not normally called
directly but can be more efficient where the response vector and
design mattrix have already been calculated.
If more than one of etastart, start and mustart
is specified, the first in the list will be used. It is often
advisable to supply starting values for a quasi family,
and also for families with unusual links such as gaussian("log").
All of weights, subset, offset, etastart
and mustart are evaluated in the same way as variables in
formula, that is first in data and then in the
environment of formula.
For the background to warning messages about ‘fitted probabilities numerically 0 or 1 occurred’ for binomial GLMs, see Venables & Ripley (2002, pp. 197--8).
Hastie, T. J. and Pregibon, D. (1992) Generalized linear models. Chapter 6 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer.
anova.glm, summary.glm, etc. for
glm methods,
and the generic functions anova, summary,
effects, fitted.values,
and residuals. lm for non-generalized linear models (which SAS
calls GLMs, for ‘general’ linear models).
loglin for fitting
log-linear models (which binomial and Poisson GLMs are) to contingency
tables.
## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
glm.D93 <- gpuGlm(counts ~ outcome + treatment, family=poisson())
anova(glm.D93)
summary(glm.D93)
# A Gamma example, from McCullagh & Nelder (1989, pp. 300-2)
clotting <- data.frame(
u = c(5,10,15,20,30,40,60,80,100),
lot1 = c(118,58,42,35,27,25,21,19,18),
lot2 = c(69,35,26,21,18,16,13,12,12))
summary(gpuGlm(lot1 ~ log(u), data=clotting, family=Gamma))
summary(gpuGlm(lot2 ~ log(u), data=clotting, family=Gamma))
Run the code above in your browser using DataLab