poissonff                package:VGAM                R Documentation

_P_o_i_s_s_o_n _F_a_m_i_l_y _F_u_n_c_t_i_o_n

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

     Family function for a generalized linear model fitted to Poisson
     responses. The dispersion parameters may be known or unknown.

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

     poissonff(link = "loge", dispersion = 1,
               onedpar = FALSE, parallel = FALSE, zero = NULL)

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

    link: Link function. See 'Links' for more choices.

dispersion: Dispersion parameter. By default, maximum likelihood is
          used to estimate the model because it is known. However, the
          user can specify 'dispersion = 0' to have it estimated, or
          else specify a known positive value (or values if the
          response is a matrix-one value per column).

 onedpar: One dispersion parameter? If the response is a matrix, then a
          separate dispersion parameter will be computed for each
          response (column), by default. Setting 'onedpar=TRUE' will
          pool them so that there is only one dispersion parameter to
          be estimated.

parallel: A logical or formula. Used only if the response is a matrix.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only.  The values must
          be from the set {1,2,...,M}, where M is the number of columns
          of the matrix response.

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

     M defined above is the number of linear/additive predictors.

     If the dispersion parameter is unknown, then the resulting
     estimate is not fully a maximum likelihood estimate.

     A dispersion parameter that is less/greater than unity corresponds
     to under-/over-dispersion relative to the Poisson model. 
     Over-dispersion is more common in practice.

     When fitting a Quadratic RR-VGLM (see 'cqo'), the response is a
     matrix of M, say, columns (e.g., one column per species). Then
     there will be M dispersion parameters (one per column of the
     response matrix) if 'dispersion=0' and 'onedpar=FALSE'.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm', 'vgam', 'rrvglm',
     'cqo', and 'cao'.

_W_a_r_n_i_n_g:

     With a multivariate response, assigning a known dispersion
     parameter for _each_ response is not handled well yet.  Currently,
     only a single known dispersion parameter is handled well.

_N_o_t_e:

     This function will handle a matrix response automatically.

     The call 'poissonff(dispersion=0, ...)' is equivalent to
     'quasipoissonff(...)'.  The latter was written so that R users of
     'quasipoisson()' would only need to add a  ``'ff''' to the end of
     the family function name.

     Regardless of whether the dispersion parameter is to be estimated
     or not, its value can be seen from the output from the 'summary()'
     of the object.

_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', 'quasipoissonff', 'zipoisson', 'loge', 'polf', 'rrvglm',
     'cqo', 'cao', 'binomialff', 'quasibinomialff', 'poisson'.

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

     poissonff()

     n = 100
     x2 = rnorm(n)
     x3 = rnorm(n)
     x4 = rnorm(n)
     lv1 = 0 + x3 - 2*x4
     lambda1 = exp(3 - 0.5 * (lv1-0)^2)
     lambda2 = exp(2 - 0.5 * (lv1-1)^2)
     lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2)
     y1 = rpois(n, lambda1)
     y2 = rpois(n, lambda2)
     y3 = rpois(n, lambda3)
     p1 = cqo(cbind(y1,y2,y3) ~ x2 + x3 + x4, poissonff, EqualTol=FALSE,
              ITol=FALSE)
     summary(p1)  # # Three dispersion parameters are all unity
     ## Not run: 
     lvplot(p1, y=TRUE, lcol=2:4, pch=2:4, pcol=2:4, rug=FALSE)
     ## End(Not run)

