rhobit                 package:VGAM                 R Documentation

_R_h_o_b_i_t _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 rhobit link transformation, including its inverse and
     the first two derivatives.

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

     rhobit(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: Optional list. Extra argument for passing in additional
          information. Values of 'theta' which are less than or equal
          to -1 can be replaced by the 'bminvalue' component of the
          list 'earg' before computing the link function value. Values
          of 'theta' which are greater than or equal to 1 can be
          replaced by the 'bmaxvalue' component of the list 'earg'
          before computing the link function 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 'rhobit' link function is commonly used for parameters that
     lie between -1 and 1.  Numerical values of 'theta' close to -1 or
     1 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 rhobit of 'theta', i.e., 'log((1 + theta)/(1
     - theta))' when 'inverse = FALSE', and if 'inverse = TRUE' then
     '(exp(theta) - 1)/(exp(theta) + 1)'.

     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 -1 or 1.
     One way of overcoming this is to use 'earg'.

     The correlation parameter of a standard bivariate normal
     distribution lies between -1 and 1, therefore this function can be
     used for modelling this parameter as a function of explanatory
     variables.

     The link function 'rhobit' is very similar to 'fisherz', e.g.,
     just twice the value of 'fisherz'.

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

     Thomas W. Yee

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

     Documentation accompanying the 'VGAM' package at <URL:
     http://www.stat.auckland.ac.nz/~yee> contains further information
     and examples.

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

     'Links', 'binom2.rho', 'fisherz'.

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

     theta = seq(-0.99, 0.99, by=0.01)
     y = rhobit(theta)
     ## Not run: 
     plot(theta, y, type="l", las=1, ylab="", main="rhobit(theta)")
     abline(v=0, h=0, lty=2)
     ## End(Not run)

     x = c(seq(-1.02, -0.98, by=0.01), seq(0.97, 1.02, by=0.01))
     rhobit(x)  # Has NAs
     rhobit(x, earg=list(bminvalue= -1 + .Machine$double.eps,
                         bmaxvalue=  1 - .Machine$double.eps))  # Has no NAs

