betageometric              package:VGAM              R Documentation

_B_e_t_a-_g_e_o_m_e_t_r_i_c _D_i_s_t_r_i_b_u_t_i_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:

     Maximum likelihood estimation for the beta-geometric distribution.

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

     betageometric(lprob="logit", lshape="loge",
                   eprob=list(), eshape=list(),
                   iprob = NULL, ishape = 0.1,
                   moreSummation=c(2,100), tolerance=1.0e-10, zero=NULL)

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

lprob, lshape: Parameter link functions applied to the parameters prob
          and phi (called 'prob' and 'shape' below). The former lies in
          the unit interval and the latter is positive. See 'Links' for
          more choices.

eprob, eshape: List. Extra argument for each of the links. See 'earg'
          in 'Links' for general information.

iprob, ishape: Numeric.  Initial values for the two parameters. A
          'NULL' means a value is computed internally.

moreSummation: Integer, of length 2.  When computing the expected
          information matrix a series summation from 0 to
          'moreSummation[1]*max(y)+moreSummation[2]' is made, in which
          the upper limit is an approximation to infinity. Here, 'y' is
          the response.

tolerance: Positive numeric.  When all terms are less than this then
          the series is deemed to have converged.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. If used, the
          value must be from the set {1,2}.

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

     A random variable Y has a 2-parameter beta-geometric distribution
     if P(Y=y) = prob * (1-prob)^y for y=0,1,2,... where prob are
     generated from a standard beta distribution with shape parameters
     'shape1' and 'shape2'. The parameterization here is to focus on
     the parameters prob and  phi = 1/(shape1+shape2), where phi is
     'shape'. The default link functions for these ensure that the
     appropriate range of the parameters is maintained. The mean of Y
     is E(Y) =  shape2 / (shape1-1) = (1-prob) / (prob-phi).

     The geometric distribution is a special case of the beta-geometric
     distribution with phi=0 (see 'geometric'). However, fitting data
     from a geometric distribution may result in numerical problems
     because the estimate of log(phi) will 'converge' to '-Inf'.

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

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

_N_o_t_e:

     The first iteration may be very slow; if practical, it is best for
     the 'weights' argument of 'vglm' etc. to be used rather than
     inputting a very long vector as the response, i.e., 'vglm(y ~ 1,
     ..., weights=wts)' is to be preferred over 'vglm(rep(y, wts) ~ 1,
     ...)'. If convergence problems occur try inputting some values of
     argument 'ishape'.

     If an intercept-only model is fitted then the 'misc' slot of the
     fitted object has list components 'shape1' and 'shape2'.

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

     T. W. Yee

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

     Paul, S. R. (2005) Testing goodness of fit of the geometric
     distribution: an application to human fecundability data. _Journal
     of Modern Applied Statistical Methods_, *4*, 425-433.

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

     'geometric', 'betaff', 'rbetageom'.

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

     y = 0:11; wts = c(227,123,72,42,21,31,11,14,6,4,7,28)
     fit  = vglm(y ~ 1, fam=betageometric, weight=wts, trace=TRUE)
     fitg = vglm(y ~ 1, fam=    geometric, weight=wts, trace=TRUE)
     coef(fit, matrix=TRUE)
     Coef(fit)
     diag(vcov(fit, untrans=TRUE))^0.5
     fit@misc$shape1
     fit@misc$shape2
     # Very strong evidence of a beta-geometric:
     1-pchisq(2*(logLik(fit)-logLik(fitg)), df=1)

