varConstPower              package: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 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.

_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
          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.

_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:

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

