R: Fitting Order-Restricted Generalized Linear Models
orglm.fit
R Documentation
Fitting Order-Restricted Generalized Linear Models
Description
orglm.fit is used to fit generalized linear models with
restrictions on the parameters, specified by giving a description of the linear predictor, a description of the error
distribution, and a description of a matrix with linear
constraints. The quadprog package is used to apply linear
constraints on the parameter vector.
x is a design matrix of dimension
n * p, and y is a vector of observations of length
n.
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 family for details of
family functions.)
weights
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be NULL or a numeric vector.
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. For orglm.fit this is passed to
glm.control.
intercept
logical. Should an intercept be included in the
null model?
constr
a matrix with linear constraints. The columns of this matrix
should correspond to the columns of the design matrix.
rhs
right hand side of the linear constraint
formulation. A numeric vector with a length corresponding to the
rows of constr.
nec
Number of equality constrints. The first nec
constraints defined in constr are treated as equality
constraints; the remaining ones are inequality constraints.
Details
Non-NULLweights 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.
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").
For the background to warning messages about ‘fitted probabilities
numerically 0 or 1 occurred’ for binomial GLMs, see Venables &
Ripley (2002, pp. 197–8).
Value
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 NA.
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 family object used.
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.
null.deviance
The deviance for the null model, comparable with
deviance. The null model will include the offset, and an
intercept if there is one in the model. Note that this will be
incorrect if the link function depends on the data other than
through the fitted mean: specify a zero offset to force a correct
calculation.
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
1s if none were.
df.residual
the residual degrees of freedom of the
unconstrained model.
df.null
the residual degrees of freedom for the null model.
y
if requested (the default) the y vector
used. (It is a vector even for a binomial model.)
converged
logical. Was the IWLS algorithm judged to have converged?
boundary
logical. Is the fitted value on the boundary of the
attainable values?
Author(s)
Modification of the original glm.fit by Daniel Gerhard.
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).
References
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.