This function is a constructor for the varConstPower class,
representing a constant plus power variance function
structure. Letting \(v\) denote the variance covariate and
\(\sigma^2(v)\) denote the variance function evaluated at
\(v\), the constant plus power variance function is defined as
\(\sigma^2(v) = (\theta_1 + |v|^\theta_2)^2\), where \(\theta_1,\theta_2\) are the variance
function coefficients. When a grouping factor is present, different
\(\theta_1,\theta_2\) are used for each factor level.
varConstPower(const, power, form, fixed)a varConstPower object representing a constant plus power
variance function structure, also inheriting from class
varFunc.
optional numeric vectors, or lists of numeric
values, with, respectively, the coefficients for the constant
and the power terms. Both arguments must have length one, unless a
grouping factor is specified in form. If either argument has
length greater than one, it must have names which identify its
elements to the levels of the grouping factor defined in
form. If a grouping factor is present in
form and the argument has length one, its value will be
assigned to all grouping levels. Only positive values are allowed
for const. Default is numeric(0), which
results in a vector of zeros of appropriate length being assigned to
the coefficients when object is initialized (corresponding
to constant variance equal to one).
an optional one-sided formula of the form ~ v, or
~ v | g, specifying a variance covariate v and,
optionally, a grouping factor g for the coefficients. The
variance covariate must evaluate to a numeric vector and may involve
expressions using ".", representing a fitted model object
from which fitted values (fitted(.)) and residuals
(resid(.)) can be extracted (this allows the variance
covariate to be updated during the optimization of an object
function). When a grouping factor is present in form,
a different coefficient value is used for each of its
levels. Several grouping variables may be
simultaneously specified, separated by the * operator, as
in ~ v | g1 * g2 * g3. In this case, the levels of each
grouping variable are pasted together and the resulting factor is
used to group the observations. Defaults to ~ fitted(.)
representing a variance covariate given by the fitted values of a
fitted model object and no grouping factor.
an optional list with components const and/or
power, consisting of numeric vectors, or lists of numeric
values, specifying the values at which some or all of the
coefficients in the variance function should be fixed. If a grouping
factor is specified in form, the components of fixed
must have names identifying which coefficients are to be
fixed. Coefficients included in fixed are not allowed to vary
during the optimization of an objective function. Defaults to
NULL, corresponding to no fixed coefficients.
José Pinheiro and Douglas Bates bates@stat.wisc.edu
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.
varClasses,
varWeights.varFunc,
coef.varConstPower
vf1 <- varConstPower(1.2, 0.2, form = ~age|Sex)
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