glmc {glmc} | R Documentation |
Fitting Generalised Linear Models Subject to Population Constraints
Description
glmc
is used to fit generalised linear models
where the parameters are subject to population constraints.
The model is specified by giving a symbolic description of
the linear predictor, a description of the error distribution,
and a matrix of constraints on the parameters.
Usage
glmc(formula,family = gaussian, data, na.action,
start = NULL,etastart, mustart, offset,control = glmc.control(...),
model = TRUE,glm.method= "glm.fit",optim.method="Nelder-Mead",
emplik.method="Owen",optim.hessian=FALSE,x = FALSE, y = TRUE,
Amat=NULL, confn=NULL,...)
Arguments
formula |
a symbolic description of the model to be fit. The details of model specification are given below. |
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 containing the variables
in the model. By default the variables are taken from
|
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. |
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. |
glm.method |
the method to be used in fitting the model.
The default method |
emplik.method |
the method used to maximise the empirical likelihood to compute the weights. The default is |
optim.method |
the method used to maximise over the parameters. See |
optim.hessian |
Logical. If True returns a numerically calculated Hessian Matrix from the optim step. |
x , y |
For For |
Amat |
a matrix of population constraints on the parameters. |
confn |
a function returning the value of the population constraints on the parameter. Allows parameter dependent population constraints. |
... |
further arguments passed to or from other methods. |
Details
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
.
A terms specification of the form
first + second
indicates all the terms in first
together
with all the terms in second
with 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
.
glmc
uses closely follows glm
, uses glm.fit
, optim
and el.test
form the emplik
library.
If more than one of etastart
, start
and mustart
is specified, the first in the list will be used.
Value
glmc
returns an object of class inheriting from "glmc"
which inherits from the class "lm"
. See later in this section.
The generic accessor functions coefficients
,
effects
, fitted.values
and residuals
can be used to
extract various useful features of the value returned by glmc
.
An object of class "glmc"
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. |
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 maximised log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. |
aic |
Akaike's An Information Criterion, minus twice the maximised log-likelihood plus twice the number of coefficients (so assuming that the dispersion is known.) |
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 from the glm step (if there is one). |
final.weights |
the weights maximising the empirical likelihood |
df.residual |
the residual degrees of freedom. |
df.null |
the residual degrees of freedom for the null model. |
y |
the |
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 |
glm.method |
the name of the fitter function used in the final |
emplik.method |
the name of the method used to maximise the empirical likelihood. |
optim.method |
the name of the method supplied to the optim function for the outer maximisation over the parameters. |
.
xlevels |
(where relevant) a record of the levels of the factors used in fitting. |
In addition, non-empty fits will have components qr
, R
and effects
relating to the final weighted linear fit.
Objects of class "glmc"
are normally of class c("glmc","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 "glmc"
such as
residuals
and weights
do not just pick out
the component of the fit with the same name. In-fact no "type"
specification in weights
retirns the weights which maximises the empirical likelihood. A call of wieghts with type="prior"
returns a vector of 1 of length equaling the number of odsevations.
Author(s)
The R implementation of glmc
is written by Sanjay Chaudhuri
and Mark S Handcock at National University of Singapore and University of Washington, Seattle respectively.
References
Owen, A. B. (2001) Empirical Likelihood. Boca Raton, Fla : Chapman \& Hall/CRC.
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.
See Also
glmc
methods,
and the generic functions anova
, summary
,
effects
, fitted.values
,
and residuals
. optim
, el.test
, the fitting procedure used by glmc
. Further, lm
for non-generalised linear models.
Examples
library(glmc)
#Specify the data.
n <- rbind(c(5903,230),c(5157,350))
mat <- matrix(0,nrow=sum(n),ncol=2)
mat <- rbind(matrix(1,nrow=n[1,1],ncol=1)%*%c(0,0),
matrix(1,nrow=n[1,2],ncol=1)%*%c(0,1),
matrix(1,nrow=n[2,1],ncol=1)%*%c(1,0),
matrix(1,nrow=n[2,2],ncol=1)%*%c(1,1))
#Specifying the population constraints.
gfr <- .06179*matrix(1,nrow=nrow(mat),ncol=1)
g <- matrix(1,nrow=nrow(mat),ncol=1)
amat <- matrix(mat[,2]*g-gfr,ncol=1)
# Method 1. Defining constraints in the data frame.
hrh <- data.frame(birth=mat[,2], child=mat[,1], constraints=amat)
gfit <- glmc(birth~child, data=hrh, family="binomial",emplik.method="Owen",
control=glmc.control(maxit.glm=10,maxit.weights=200,
itertrace.weights=TRUE,gradtol.weights=10^(-6)))
summary.glmc(gfit)
# Method 2. Defining constraints through a matrix.
gfit<- glmc(mat[,2]~mat[,1],family=binomial(link=logit),
emplik.method="Owen",control=glmc.control(maxit.glm=10,
maxit.weights=200,itertrace.weights=TRUE,gradtol.weights=10^(-10)),
Amat=amat,confn=NULL)
summary.glmc(gfit)
## Not run:
# Method 3. Defining constraints through a function.
fn <- function(t,Y,X){
grf <- .06179*matrix(1,nrow=nrow(as.matrix(X)),ncol=1)
g <- matrix(1,nrow=nrow(X),ncol=1)
amat <- matrix(Y*g-grf,ncol=1)
return(amat)
}
gfit <- glmc(birth~child,data=hrh,family=binomial(link=logit),
optim.method="BFGS",emplik.method="Owen",
control=glmc.control(maxit.glm=10,maxit.optim=10^(8),
reltol.optim=10^(-10),trace.optim=9,REPORT.optim=1,
maxit.weights=200,gradtol.weights=10^(-6),itertrace.weights=FALSE),
optim.hessian=TRUE,Amat=NULL,confn=fn)
summary.glmc(gfit)
## End(Not run)