odTest                 package:pscl                 R Documentation

_l_i_k_e_l_i_h_o_o_d _r_a_t_i_o _t_e_s_t _f_o_r _o_v_e_r-_d_i_s_p_e_r_s_i_o_n _i_n _c_o_u_n_t _d_a_t_a

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

     Compares the log-likelihoods of a negative binomial regression
     model and a Poisson regression model.

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

     odTest(glmobj, alpha=.05, digits = max(3, getOption("digits") - 3))

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

  glmobj: an object of class 'negbin' produced by 'glm.nb'

   alpha: significance level of over-dispersion test

  digits: number of digits in printed output

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

     The negative binomial model relaxes the assumption in the Poisson
     model that the (conditional) variance equals the (conditional)
     mean, by estimating one extra parameter.  A likelihood ratio (LR)
     test can be used to test the null hypothesis that the restriction
     implicit in the Poisson model is true. The LR test-statistic has a
     non-standard distribution, even asymptotically, since the negative
     binomial over-dispersion parameter (called 'theta' in 'glm.nb') is
     restricted to be positive.  The asymptotic distribution of the LR
     (likelihood ratio) test-statistic has probability mass of one half
     at zero, and a half chi-square (1) distribution above zero.  This
     means that if testing at the alpha = .05 level, one should not
     reject the null unless the LR test statistic exceeds the critical
     value associated with the 2 alpha = .10 level; this LR test
     involves just one parameter restriction, so the critical value of
     the test statistic at the p = .05 level is 2.7, instead of the
     usual 3.8 (i.e., the .90 quantile of the chi-square (1)
     distribution, versus the .95 quantile).

     A Poisson model is run using 'glm' with family set to
     'link{poisson}', using the 'formula' in the negbin model object
     passed as input.  The 'logLik' functions are used to extract the
     log-likelihood for each model.

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

     None; prints results and returns silently

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

     Simon Jackman jackman@stanford.edu.  John Fox noted an error in an
     earlier version.

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

     A. Colin Cameron and Pravin K. Trivedi (1998) _Regression analysis
     of count data_. New York: Cambridge University Press.

     Lawless, J. F. (1987) "Negative Binomial and Mixed Poisson
     Regressions." _The Canadian Journal of Statistics_. 15:209-225.

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

     'glm.nb', 'logLik'

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

     data(bioChemists)
     require(MASS)
     modelnb <- glm.nb(art ~ .,
                      data=bioChemists,
                      trace=TRUE)
     odTest(modelnb)

