

varExp(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 struc-
     ture. Letting v denote the variance covariate and s2(v)
     denote the variance function evaluated at v, the expo-
     nential 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 group-
          ing 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 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 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 `var-
     Func'.

_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_:

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

