gamma.shape               package:MASS               R Documentation

_E_s_t_i_m_a_t_e _t_h_e _S_h_a_p_e _P_a_r_a_m_e_t_e_r _o_f _t_h_e _G_a_m_m_a _D_i_s_t_r_i_b_u_t_i_o_n _i_n _a _G_L_M _F_i_t

_D_e_s_c_r_i_p_t_i_o_n:

     Find the maximum likelihood estimate of the shape parameter of the
     gamma distribution after fitting a 'Gamma' generalized linear
     model.

_U_s_a_g_e:

     ## S3 method for class 'glm':
     gamma.shape(object, it.lim = 10,
                 eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)

_A_r_g_u_m_e_n_t_s:

  object: Fitted model object from a 'Gamma' family or 'quasi' family
          with 'variance = "mu^2"'. 

  it.lim: Upper limit on the number of iterations. 

 eps.max: Maximum discrepancy between approximations for the iteration
          process to continue. 

 verbose: If 'TRUE', causes successive iterations to be printed out. 
          The initial estimate is taken from the deviance. 

     ...: further arguments passed to or from other methods. 

_D_e_t_a_i_l_s:

     A glm fit for a Gamma family correctly calculates the maximum
     likelihood estimate of the mean parameters but provides only a
     crude estimate of the dispersion parameter.  This function takes
     the results of the glm fit and solves the maximum likelihood
     equation for the reciprocal of the dispersion parameter, which is
     usually called the shape (or exponent) parameter.

_V_a_l_u_e:

     List of two components

   alpha: the maximum likelihood estimate 

      SE: the approximate standard error, the square-root of the
          reciprocal of the observed information. 

_R_e_f_e_r_e_n_c_e_s:

     Venables, W. N. and Ripley, B. D. (2002) _Modern Applied
     Statistics with S._ Fourth edition.  Springer.

_S_e_e _A_l_s_o:

     'gamma.dispersion'

_E_x_a_m_p_l_e_s:

     clotting <- data.frame(
         u = c(5,10,15,20,30,40,60,80,100),
         lot1 = c(118,58,42,35,27,25,21,19,18),
         lot2 = c(69,35,26,21,18,16,13,12,12))
     clot1 <- glm(lot1 ~ log(u), data = clotting, family = Gamma)
     gamma.shape(clot1)
     ## Not run: 
     Alpha: 538.13
        SE: 253.60
     ## End(Not run)
     gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn,
               quasi(link=log, variance="mu^2"), quine,
               start = c(3, rep(0,31)))
     gamma.shape(gm, verbose = TRUE)
     ## Not run: 
     Initial estimate: 1.0603
     Iter.  1  Alpha: 1.23840774338543
     Iter.  2  Alpha: 1.27699745778205
     Iter.  3  Alpha: 1.27834332265501
     Iter.  4  Alpha: 1.27834485787226

     Alpha: 1.27834
        SE: 0.13452
     ## End(Not run)
     summary(gm, dispersion = gamma.dispersion(gm))  # better summary