

   CCoonnssttaanntt PPlluuss PPoowweerr VVaarriiaannccee FFuunnccttiioonn

        varConstPower(const, power, form, fixed)

   AArrgguummeennttss::

   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 iden-
             tify 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 residu-
             als (`resid(.)') can be extracted (this allows the
             variance covariate to be updated during the opti-
             mization of an object function). When a grouping
             factor is present in `form', a different coeffi-
             cient value is used for each of its levels. Sev-
             eral 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 observa-
             tions. 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', corre-
             sponding to no fixed coefficients.

   DDeessccrriippttiioonn::

        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 evalu-
        ated 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.

   VVaalluuee::

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

   AAuutthhoorr((ss))::

        Jose Pinheiro and Douglas Bates

   SSeeee AAllssoo::

        `varWeights.varFunc', `coef.varConstPower'

   EExxaammpplleess::

        library(lme)
        vf1 <- varConstPower(1.2, 0.2, form = ~age|Sex)

