tweedie               package:statmod               R Documentation

_T_w_e_e_d_i_e _G_e_n_e_r_a_l_i_z_e_d _L_i_n_e_a_r _M_o_d_e_l_s

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

     Produces a generalized linear model family object with any power
     variance function and any power link. Includes the Gaussian,
     Poisson, gamma and inverse-Gaussian families as special cases.

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

     tweedie(var.power=0, link.power=1-var.power)

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

var.power: index of power variance function

link.power: index of power link function. 'link.power=0' produces a
          log-link. Defaults to the canonical link, which is
          '1-var.power'.

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

     This function provides access to a range of generalized linear
     model response distributions which are not otherwise provided by
     R, or any other package for that matter. It is also useful for
     accessing distribution/link combinations which are disallowed by
     the R 'glm' function.

     Let mu_i = E(y_i) be the expectation of the ith response. We
     assume that

                mu_i^q = x_i^Tb, var(y_i) = phi mu_i^p


     where x_i is a vector of covariates and b is a vector of
     regression cofficients, for some phi, p and q. This family is
     specified by 'var.power = p' and 'link.power = q'. A value of zero
     for q is interpreted as log(mu_i) = x_i^Tb. 

     The variance power p characterizes the distribution of the
     responses y. The following are some special cases:

        *p*    *Response distribution*
         0     Normal
         1     Poisson
       (1, 2)  Compound Poisson, non-negative with mass at zero
         2     Gamma
         3     Inverse-Gaussian
        > 2    Stable, with support on the positive reals

     The name Tweedie has been associated with this family by Jrgensen
     in honour of M. C. K. Tweedie.

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

     A family object, which is a list of functions and expressions used
     by glm and gam in their iteratively reweighted least-squares
     algorithms. See 'family' and 'glm' in the R base help for details.

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

     Gordon Smyth

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

     Tweedie, M. C. K. (1984). An index which distinguishes between
     some important exponential families. In _Statistics: Applications
     and New Directions_. Proceedings of the Indian Statistical
     Institute Golden Jubilee International Conference. (Eds. J. K.
     Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical
     Institute.

     Jrgensen, B. (1987). Exponential dispersion models. _J. R.
     Statist. Soc._ B *49*, 127-162. 

     Smyth, G. K. (1996). Regression modelling of quantity data with
     exact zeroes. Proceedings of the Second Australia-Japan Workshop
     on Stochastic Models in Engineering, Technology and Management.
     Technology Management Centre, University of Queensland, pp.
     572-580. 

     Jrgensen, B. (1997). _Theory of Dispersion Models_, Chapman and
     Hall, London. 

     Smyth, G. K., and Verbyla, A. P., (1999). Adjusted likelihood
     methods for modelling dispersion in generalized linear models.
     _Environmetrics_ *10*, 695-709.

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

     'glm', 'family', 'dtweedie'

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

     y <- rgamma(20,shape=5)
     x <- 1:20
     # Fit a poisson generalized linear model with identity link
     glm(y~x,family=tweedie(var.power=1,link.power=1))

     # Fit an inverse-Gaussion glm with log-link
     glm(y~x,family=tweedie(var.power=3,link.power=0)) 

