nlme (version 3.1-152)

# varExp: Exponential Variance Function

## Description

This function is a constructor for the varExp class, representing an exponential variance function structure. Letting $$v$$ denote the variance covariate and $$\sigma^2(v)$$ denote the variance function evaluated at $$v$$, the exponential variance function is defined as $$\sigma^2(v) = \exp(2\theta v)$$, where $$\theta$$ is the variance function coefficient. When a grouping factor is present, a different $$\theta$$ is used for each factor level.

## Usage

varExp(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 varExp object representing an exponential 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.varExp
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