logoff                 package:VGAM                 R Documentation

_L_o_g _l_i_n_k _f_u_n_c_t_i_o_n _w_i_t_h _a_n _o_f_f_s_e_t

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

     Computes the log transformation with an offset, including its
     inverse and the first two derivatives.

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

     logoff(theta, earg = list(offset=0), 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: List. Extra argument for passing in additional information.
          The 'offset' component of the list 'earg' is the offset
          value. See 'Links' for general information about 'earg'.

 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 log-offset link function is very commonly used for parameters
     that are greater than a certain value. In particular, it is
     defined by 'log(theta+offset)' where 'offset' is the offset value.
     For example, if 'offset=0.5' then the value of 'theta' is
     restricted to be greater than -0.5.

     Numerical values of 'theta' close to '-offset' or out of range
     result in 'Inf', '-Inf', 'NA' or 'NaN'. The arguments 'short' and
     'tag' are used only if 'theta' is character.

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

     For 'deriv = 0', the log of 'theta+offset', i.e.,
     'log(theta+offset)' when 'inverse = FALSE', and if 'inverse =
     TRUE' then 'exp(theta)-offset'.

     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.

     Here, all logarithms are natural logarithms, i.e., to base _e_.

_N_o_t_e:

     The default means this function is identical to 'loge'.

     Numerical instability may occur when 'theta' is close to
     '-offset'.

_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'.

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

     ## Not run: 
     logoff(seq(-0.2, 0.5, by=0.1))
     logoff(seq(-0.2, 0.5, by=0.1), earg=list(offset=0.5))
     log(seq(-0.2, 0.5, by=0.1) + 0.5)
     ## End(Not run)

