identity                package:VGAM                R Documentation

_I_d_e_n_t_i_t_y _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 identity transformation, including its inverse and
     the first two derivatives.

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

     identity(theta, earg = list(), inverse = FALSE, deriv = 0,
              short = TRUE, tag = FALSE)
     nidentity(theta, earg = list(), inverse = 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: Extra argument for passing in additional information. Here,
          the argument is unused. 

 inverse: 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 identity link function g(theta)=theta should be available to
     every parameter estimated by the 'VGAM' library. However, it
     usually results in numerical problems because the estimates lie
     outside the permitted range. Consequently, the result may contain 
     'Inf', '-Inf', 'NA' or 'NaN'. The arguments 'short' and 'tag' are
     used only if 'theta' is character.

     The function 'nidentity' is the negative-identity link function
     and corresponds to g(theta)=-theta. This is useful for some
     models, e.g., in the literature supporting the 'egev' function it
     seems that half of the authors use xi=-k for the shape parameter
     and the other half use k instead of xi.

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

     For 'identity()': for 'deriv = 0', the identity of 'theta', i.e.,
     'theta' when 'inverse = FALSE', and if 'inverse = TRUE' then
     '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.

     For 'nidentity()': the results are similar to 'identity()' except
     for a sign change in most cases.

_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:

     'Links', 'loge', 'logit', 'probit', 'powl'.

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

     identity((-5):5) 
     identity((-5):5, deriv=1)
     identity((-5):5, deriv=2)
     nidentity((-5):5) 
     nidentity((-5):5, deriv=1)
     nidentity((-5):5, deriv=2)

