addreg.smooth {addreg}  R Documentation 
Smooth Additive Regression for Discrete Data
Description
addreg.smooth
fits additive (identitylink) Poisson, negative binomial
and binomial regression models using a stable EM algorithm. It provides additional
flexibility over addreg
by allowing for semiparametric
terms.
Usage
addreg.smooth(formula, mono = NULL, family, data, standard, subset,
na.action, offset, control = list(...), model = TRUE,
model.addreg = FALSE, method = c("cem", "em"),
accelerate = c("em", "squarem", "pem", "qn"),
control.method = list(), ...)
Arguments
formula 
an object of class 
mono 
a vector indicating which terms in

family 
a description of the error distribution 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 
standard 
a numeric vector of length equal to the number of cases, where each element is a positive constant that (multiplicatively) standardises the fitted value of the corresponding element of the response vector. Ignored for binomial family (the twocolumn specification of response should be used instead). 
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 
offset 
this can be used to specify an a
priori known component to be included in the linear
predictor during fitting. This should be Ignored for binomial family; not yet implemented for negative binomial models. 
control 
list of parameters for controlling the
fitting process, passed to

model 
a logical value indicating whether the model frame (and, for binomial models, the equivalent Poisson model) should be included as a component of the returned value. 
model.addreg 
a logical value indicating whether the fitted 
method 
a character string that determines which EMtype algorithm to use
to find the MLE: 
accelerate 
a character string that determines the acceleration
algorithm to be used, (partially) matching one of 
control.method 
a list of control parameters for the acceleration algorithm, which are passed to
the If any items are not specified, the defaults are used. 
... 
arguments to be used to form the default

Details
addreg.smooth
performs the same fitting process as addreg
,
providing a stable maximum likelihood estimation procedure for identitylink
Poisson, negative binomial or binomial models, with the added flexibility of allowing semiparametric
B
and Iso
terms (note that addreg.smooth
will stop with an
error if no semiparametric terms are specified in the righthand side of the formula
;
addreg
should be used instead).
The method partitions the parameter space associated with the semiparametric part of the
model into a sequence of constrained parameter spaces, and defines a fully parametric
addreg
model for each. The model with the highest loglikelihood is the MLE for
the semiparametric model (see Donoghoe and Marschner, 2015).
Acceleration of the EM algorithm can be achieved through the
methods of the turboEM package, specified
through the accelerate
argument. However, note that these
methods do not have the guaranteed convergence of the standard
EM algorithm, particularly when the MLE is on the boundary of
its (possibly constrained) parameter space.
Value
An object of class "addreg.smooth"
, which contains the same objects as class
"addreg"
(the same as "glm"
objects, without contrasts
,
qr
, R
or effects
components), as well as:
model.addreg 
if 
xminmax.smooth 
the minimum and maximum observed values for each of the smooth terms in the model, to help define the covariate space. 
full.formula 
the component from 
knots 
a named list containing the knot vectors for each of the smooth terms in the model. 
Author(s)
Mark W. Donoghoe markdonoghoe@gmail.com
References
Donoghoe, M. W. and I. C. Marschner (2015). Flexible regression models for rate differences, risk differences and relative risks. International Journal of Biostatistics 11(1): 91–108.
Marschner, I. C. (2014). Combinatorial EM algorithms. Statistics and Computing 24(6): 921–940.
See Also
Examples
## Simple example
dat < data.frame(x1 = c(3.2,3.3,3.4,7.9,3.8,0.7,2.0,5.4,8.4,3.0,1.8,5.6,5.5,9.0,8.2),
x2 = c(1,0,0,1,0,1,0,0,0,0,1,0,1,1,0),
n = c(6,7,5,9,10,7,9,6,6,7,7,8,6,8,10),
y = c(2,1,2,6,3,1,2,2,4,4,1,2,5,7,7))
m1 < addreg.smooth(cbind(y, ny) ~ B(x1, knot.range = 1:3) + factor(x2), mono = 1,
data = dat, family = binomial, trace = 1)
plot(m1, at = data.frame(x2 = 0:1))
points(dat$x1, dat$y / dat$n, col = rainbow(2)[dat$x2 + 1], pch = 20)