nlme (version 3.1-152)

# varConstPower: 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 $$\sigma^2(v)$$ 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.

## 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.

## References

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

varClasses, varWeights.varFunc, coef.varConstPower
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