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)`

const, power

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).

form

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.

fixed

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.

a `varConstPower`

object representing a constant plus power
variance function structure, also inheriting from class
`varFunc`

.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.

```
# NOT RUN {
vf1 <- varConstPower(1.2, 0.2, form = ~age|Sex)
# }
```

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