Description Usage Arguments Details Value Author(s) References See Also Examples
Most of this documentation is copied from R's documentation for 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.
1 2 3 4 5 6 7 8 | 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 |
an object of class |
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 |
data |
an optional data frame, list or environment (or object
coercible by |
weights |
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be |
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 |
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 |
useSingle |
whether to use single precision arithmetic on the gpu. Only the 'TRUE' option is implemented so far. |
control |
a list of parameters for controlling the fitting
process. See the documentation for |
model |
a logical value indicating whether model frame should be included as a component of the returned value. |
method |
the method to be used in fitting the model.
The default method |
x, y |
For For |
contrasts |
an optional list. See the |
intercept |
logical. Should an intercept be included in the null model? |
... |
For For |
A typical predictor has the form 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).
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:
coefficients |
a named vector of coefficients |
residuals |
the working residuals, that is the residuals
in the final iteration of the IWLS fit. Since cases with zero
weights are omitted, their working residuals are |
fitted.values |
the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function. |
rank |
the numeric rank of the fitted linear model. |
family |
the |
linear.predictors |
the linear fit on link scale. |
deviance |
up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. |
aic |
A version of Akaike's An Information Criterion,
minus twice the maximized log-likelihood plus twice the number of
parameters, computed by the |
null.deviance |
The deviance for the null model, comparable with
|
iter |
the number of iterations of IWLS used. |
weights |
the working weights, that is the weights in the final iteration of the IWLS fit. |
prior.weights |
the weights initially supplied, a vector of
|
df.residual |
the residual degrees of freedom. |
df.null |
the residual degrees of freedom for the null model. |
y |
if requested (the default) the |
x |
if requested, the model matrix. |
model |
if requested (the default), the model frame. |
converged |
logical. Was the IWLS algorithm judged to have converged? |
boundary |
logical. Is the fitted value on the boundary of the attainable values? |
call |
the matched call. |
formula |
the formula supplied. |
terms |
the |
data |
the |
offset |
the offset vector used. |
control |
the value of the |
method |
the name of the fitter function used, currently always
|
contrasts |
(where relevant) the contrasts used. |
xlevels |
(where relevant) a record of the levels of the factors used in fitting. |
na.action |
(where relevant) information returned by
|
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.
The original R implementation of glm
was written by Simon
Davies working for Ross Ihaka at the University of Auckland, but has
since been extensively re-written by members of the R Core team.
The design was inspired by the S function of the same name described in Hastie & Pregibon (1992).
This function was adapted for Nvidia's CUDA–supporting GPGPUs by
Mark Seligman at Rapid Biologics LLC.
http://www.rapidbiologics.com
Dobson, A. J. (1990) An Introduction to Generalized Linear Models. London: Chapman and Hall.
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ## 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))
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.