reciprocal               package:VGAM               R Documentation

_R_e_c_i_p_r_o_c_a_l _l_i_n_k _f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the reciprocal transformation, including its inverse and
     the first two derivatives.

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

     reciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
             short = TRUE, tag = FALSE)
     nreciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
             short = TRUE, tag = FALSE)

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

   theta: Numeric or character. See below for further details.

    earg: Optional list. Extra argument for passing in additional
          information. Values of 'theta' which are equal to 0 can be
          replaced by the 'bvalue' component of the list 'earg' before
          computing the link function value. The component name
          'bvalue' stands for ``boundary value''. See 'Links' for
          general information about 'earg'.

inverse.arg: Logical. If 'TRUE' the inverse function is computed

   deriv: Order of the derivative. Integer with value 0, 1 or 2.

   short: Used for labelling the 'blurb' slot of a 'vglmff-class'
          object.

     tag: Used for labelling the linear/additive predictor in the
          'initialize' slot of a 'vglmff-class' object. Contains a
          little more information if 'TRUE'.

_D_e_t_a_i_l_s:

     The 'reciprocal' link function is a special case of the power link
     function.  Numerical values of 'theta' close to 0 result in 'Inf',
     '-Inf', 'NA' or 'NaN'.  The arguments 'short' and 'tag' are used
     only if 'theta' is character.

     The 'nreciprocal' link function computes the negative reciprocal,
     i.e., -1/theta.

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

     For 'reciprocal': for 'deriv = 0', the reciprocal of 'theta',
     i.e., '1/theta' when 'inverse = FALSE', and if 'inverse = TRUE'
     then '1/theta'. For 'deriv = 1', then the function returns _d_
     'theta' / _d_ 'eta' as a function of 'theta' if 'inverse = FALSE',
     else if 'inverse = TRUE' then it returns the reciprocal.

_N_o_t_e:

     Numerical instability may occur when 'theta' is close to 0.

_A_u_t_h_o_r(_s):

     Thomas W. Yee

_R_e_f_e_r_e_n_c_e_s:

     McCullagh, P. and Nelder, J. A. (1989) _Generalized Linear
     Models_, 2nd ed. London: Chapman & Hall.

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

     'identity', 'powl'.

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

     reciprocal(1:5)
     reciprocal(1:5, inverse=TRUE, deriv=2)
     nreciprocal(1:5)
     nreciprocal(1:5, inverse=TRUE, deriv=2)

     x = (-3):3
     reciprocal(x)  # Has Inf
     reciprocal(x, earg=list(bvalue= .Machine$double.eps))  # Has no Inf

