varExp                 package:nlme                 R Documentation

_E_x_p_o_n_e_n_t_i_a_l _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 `varExp' class,
     representing an exponential variance function structure. Letting v
     denote the variance covariate and s2(v) denote the variance
     function evaluated at v, the exponential variance function is
     defined as s2(v) = exp(2* t * v), where t is the variance function
     coefficient. When a grouping factor is present, a different t is
     used for each factor level.

_U_s_a_g_e:

     varExpon(value, form, fixed)

_A_r_g_u_m_e_n_t_s:

   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.

_V_a_l_u_e:

     a `varExp' object representing an exponential 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.varExp'

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

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

