varConstPower {nlme} R Documentation

## Constant Plus Power Variance Function

### Description

This function is a constructor for the `varConstPower` class, representing a constant plus power variance function structure. Letting v denote the variance covariate and s2(v) denote the variance function evaluated at v, the constant plus power variance function is defined as s2(v) = (t1 + |v|^t2)^2, where t1, t2 are the variance function coefficients. When a grouping factor is present, different t1, t2 are used for each factor level.

### Usage

```varConstPower(const, power, form, fixed)
```

### Arguments

 `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.

### Value

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

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

`varWeights.varFunc`, `coef.varConstPower`
```vf1 <- varConstPower(1.2, 0.2, form = ~age|Sex)