Fitting OrderRestricted 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.
Usage
1 2 3 4 
Arguments
x, y 

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 
weights 
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be 
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 
control 
a list of parameters for controlling the fitting
process. For 
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 
nec 
Number of equality constrints. The first 
Details
NonNULL
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 unitweight 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 
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 loglikelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. 
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 of the unconstrained model. 
df.null 
the residual degrees of freedom for the null model. 
y 
if requested (the default) the 
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 rewritten 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.
See Also
glm
, solve.QP