This function is a constructor for the `varPower`

class,
representing a power variance function structure. Letting
\(v\) denote the variance covariate and \(\sigma^2(v)\)
denote the variance function evaluated at \(v\), the power
variance function is defined as \(\sigma^2(v) = |v|^{2\theta}\), where \(\theta\) is the variance
function coefficient. When a grouping factor is present, a different
\(\theta\) is used for each factor level.

`varPower(value, form, fixed)`

value

an optional numeric vector, or list of numeric values,
with the variance function coefficients. `Value`

must have
length one, unless a grouping factor is specified in `form`

.
If `value`

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 `value`

has length one, its value will be
assigned to all grouping levels. 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, like
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 numeric vector, or list 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`

, `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 `varPower`

object representing a 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 <- varPower(0.2, form = ~age|Sex)
# }
```

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