

varConstPower(nlme)                          R Documentation

_C_o_n_s_t_a_n_t _P_l_u_s _P_o_w_e_r _V_a_r_i_a_n_c_e _F_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_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.

_U_s_a_g_e_:

     varConstPower(const, power, form, fixed)

_A_r_g_u_m_e_n_t_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, 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 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.

_V_a_l_u_e_:

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

_A_u_t_h_o_r_(_s_)_:

     Jose Pinheiro and Douglas Bates

_S_e_e _A_l_s_o_:

     `varWeights.varFunc', `coef.varConstPower'

_E_x_a_m_p_l_e_s_:

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

