ccoef                  package:VGAM                  R Documentation

_E_x_t_r_a_c_t _M_o_d_e_l _C_o_n_s_t_r_a_i_n_e_d/_C_a_n_o_n_i_c_a_l _C_o_e_f_f_i_c_i_e_n_t_s

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

     'ccoef' is a generic function which extracts the constrained
     (canonical) coefficients from objects returned by certain
     modelling functions.

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

     ccoef(object, ...)

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

  object: An object for which the extraction of canonical coefficients
          is meaningful. 

     ...: Other arguments fed into the specific methods function of the
          model. 

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

     For constrained quadratic and ordination models, _canonical
     coefficients_ are the elements of the *C* matrix used to form the
     latent variables.  They are highly interpretable in ecology, and
     are looked at as weights or loadings.

     They are also applicable for reduced-rank VGLMs.

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

     The value returned depends specifically on the methods function
     invoked.

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

     For QO models, there is a direct inverse relationship between the
     scaling of the latent variables (site scores) and the tolerances.
     One normalization is for the latent variables to have unit
     variance. Another normalization is for all the species' tolerances
     to be unit (provided 'EqualTolerances' is 'TRUE').  These two
     normalizations cannot simultaneously hold in general.  For rank R
     models with R>1 it becomes more complicated because the latent
     variables are also uncorrelated. An important argument when
     fitting quadratic ordination models is whether 'EqualTolerances'
     is 'TRUE' or 'FALSE'.  See Yee (2004) for details.

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

     Thomas W. Yee

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

     Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector
     generalized linear models. _Statistical Modelling_, *3*, 15-41.

     Yee, T. W. (2004) A new technique for maximum-likelihood canonical
     Gaussian ordination. _Ecological Monographs_, *74*, 685-701.

     Yee, T. W. (2006) Constrained additive ordination. _Ecology_,
     *87*, 203-213.

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

     'ccoef-method', 'ccoef.qrrvglm', 'ccoef.cao', 'coef'.

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

     data(hspider)
     set.seed(111)  # This leads to the global solution
     hspider[,1:6] = scale(hspider[,1:6]) # Standardized environmental vars
     p1 = cqo(cbind(Alopacce, Alopcune, Alopfabr, Arctlute, Arctperi,
                    Auloalbi, Pardlugu, Pardmont, Pardnigr, Pardpull,
                    Trocterr, Zoraspin) ~
              WaterCon + BareSand + FallTwig + CoveMoss + CoveHerb + ReflLux,
              fam = quasipoissonff, data = hspider, Crow1positive=FALSE)
     ccoef(p1)

