# varPower: Power Variance Function In nlme: Linear and Nonlinear Mixed Effects Models

## Description

This function is a constructor for the `varPower` class, representing a power variance function structure. Letting v denote the variance covariate and s2(v) denote the variance function evaluated at v, the power variance function is defined as s2(v) = |v|^(2*t), where t is the variance function coefficient. When a grouping factor is present, a different t is used for each factor level.

## Usage

 `1` ```varPower(value, form, fixed) ```

## Arguments

 `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.

## Value

a `varPower` object representing a power variance function structure, also inheriting from class `varFunc`.

## Author(s)

José Pinheiro and Douglas Bates [email protected]

## References

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

`varWeights.varFunc`, `coef.varPower`

## Examples

 `1` ```vf1 <- varPower(0.2, form = ~age|Sex) ```

### Example output

```
```

nlme documentation built on April 7, 2018, 5:03 p.m.