AICvlm                 package:VGAM                 R Documentation

_A_k_a_i_k_e'_s _I_n_f_o_r_m_a_t_i_o_n _C_r_i_t_e_r_i_o_n

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

     Calculates the Akaike information criterion for a fitted model
     object for which a log-likelihood value has been obtained.

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

     AICvlm(object, ..., k = 2)

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

  object: Some 'VGAM' object, for example, having class 'vglmff-class'. 

     ...: Other possible arguments fed into 'logLik' in order to
          compute the log-likelihood. 

       k: Numeric, the penalty per parameter to be used; the default is
          the classical AIC. 

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

     The following formula is used for VGLMs: -2*log-likelihood +
     k*npar, where npar represents the number of parameters in the
     fitted model, and k = 2 for the usual AIC. One could assign k =
     log(n) (n the number of observations) for the so-called BIC or SBC
     (Schwarz's Bayesian criterion).

     This code relies on the log-likelihood being defined, and
     computed, for the object. When comparing fitted objects, the
     smaller the AIC, the better the fit. The log-likelihood and hence
     the AIC is only defined up to an additive constant.

     Any estimated scale parameter (in GLM parlance) is used as one
     parameter.

     For VGAMs the nonlinear effective degrees of freedom for each
     smoothed component is used. This formula is heuristic.

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

     Returns a numeric value with the corresponding AIC (or BIC, or
     ..., depending on 'k').

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

     This code has not been double-checked. The general applicability
     of 'AIC' for the VGLM/VGAM classes has not been developed fully. 
     In particular, 'AIC' should not be run on some 'VGAM' family
     functions because of violation of certain regularity conditions,
     etc.

_N_o_t_e:

     AIC has not been defined for QRR-VGLMs yet.

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

     T. W. Yee.

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

     VGLMs are described in 'vglm-class'; VGAMs are described in
     'vgam-class'; RR-VGLMs are described in 'rrvglm-class'; 'AIC'.

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

     pneumo = transform(pneumo, let=log(exposure.time))
     (fit1 = vglm(cbind(normal, mild, severe) ~ let,
                cumulative(parallel=TRUE, reverse=TRUE), pneumo))
     coef(fit1, matrix=TRUE)
     AIC(fit1)
     (fit2 = vglm(cbind(normal, mild, severe) ~ let,
                cumulative(parallel=FALSE, reverse=TRUE), pneumo))
     coef(fit2, matrix=TRUE)
     AIC(fit2)

