Tol                   package:VGAM                   R Documentation

_T_o_l_e_r_a_n_c_e_s

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

     Generic function for the _tolerances_ of a model.

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

     Tol(object, ...)

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

  object: An object for which the computation or extraction of a
          tolerance or tolerances is meaningful. 

     ...: Other arguments fed into the specific methods function of the
          model. Sometimes they are fed into the methods function for
          'Coef'. 

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

     Different models can define an optimum in different ways. Many
     models have no such notion or definition.

     Tolerances occur in quadratic ordination, i.e., CQO or UQO. They
     have ecological meaning because a high tolerance for a species
     means the species can survive over a large environmental range
     (stenoecous species), whereas a small tolerance means the species'
     niche is small (eurycous species). Mathematically, the tolerance
     is like the variance of a normal distribution.

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

     The value returned depends specifically on the methods function
     invoked.

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

     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 tolerances to be unit. These
     two normalization cannot simultaneously hold in general. For
     rank-_R>1_ models 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.

_N_o_t_e:

     Tolerances are undefined for `linear' and additive  ordination
     models. They are well-defined for quadratic ordination models.

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

     Thomas W. Yee

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

     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:

     'Tol.qrrvglm'. 'Max', 'Opt'.

_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,
              Bestof = 2,
              fam = quasipoissonff, data = hspider, Crow1positive=FALSE)

     Tol(p1)

