acat                  package:VGAM                  R Documentation

_O_r_d_i_n_a_l _R_e_g_r_e_s_s_i_o_n _w_i_t_h _A_d_j_a_c_e_n_t _C_a_t_e_g_o_r_i_e_s _P_r_o_b_a_b_i_l_i_t_i_e_s

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

     Fits an adjacent categories regression model to an ordered
     (preferably) factor response.

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

     acat(link = "loge", parallel = FALSE, reverse = FALSE, zero = NULL)

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

     In the following, the response Y is assumed to be a factor with
     ordered values 1,2,...,M+1, so that M is the number of
     linear/additive predictors eta_j.

    link: Link function applied to the ratios of the  adjacent
          categories probabilities.  See 'Links' for more choices.

parallel: A logical, or formula specifying which terms have
          equal/unequal coefficients.

 reverse: Logical. By default, the linear/additive predictors used are
          eta_j = log(P[Y=j+1]/P[Y=j]) for j=1,...,M. If 'reverse' is
          'TRUE', then eta_j=log(P[Y=j]/P[Y=j+1]) will be used.

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

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

     By default, the log link is used because the ratio of two
     probabilities is positive.

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

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

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

     No check is made to verify that the response is ordinal.

_N_o_t_e:

     The response should be either a matrix of counts (with row sums
     that are all positive), or a factor. In both cases, the 'y' slot
     returned by 'vglm'/'vgam'/'rrvglm' is the matrix of counts.

     For a nominal (unordered) factor response, the multinomial logit
     model ('multinomial') is more appropriate.

     Here is an example of the usage of the 'parallel' argument. If
     there are covariates 'x1', 'x2' and 'x3', then 'parallel = TRUE ~
     x1 + x2 -1' and 'parallel = FALSE ~ x3' are equivalent. This would
     constrain the regression coefficients for 'x1' and 'x2' to be
     equal; those of the intercepts and 'x3' would be different.

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

     Thomas W. Yee

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

     Agresti, A. (2002) _Categorical Data Analysis_, 2nd ed. New York:
     Wiley.

     Simonoff, J. S. (2003) _Analyzing Categorical Data_, New York:
     Springer-Verlag.

     Documentation accompanying the 'VGAM' package at <URL:
     http://www.stat.auckland.ac.nz/~yee> contains further information
     and examples.

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

     'cumulative', 'cratio', 'sratio', 'multinomial', 'pneumo'.

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

     data(pneumo)
     pneumo = transform(pneumo, let=log(exposure.time))
     (fit = vglm(cbind(normal,mild,severe) ~ let, acat, pneumo))
     coef(fit, matrix=TRUE)
     constraints(fit)
     model.matrix(fit)

