sratio                 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 _S_t_o_p_p_i_n_g _R_a_t_i_o_s

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

     Fits a stopping ratio logit/probit/cloglog/cauchit/... regression
     model to an ordered (preferably) factor response.

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

     sratio(link = "logit", earg = list(),
            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 M stopping ratio probabilities. 
          See 'Links' for more choices.

    earg: List. Extra argument for the link function. See 'earg' in
          'Links' for general information.

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

 reverse: Logical. By default, the stopping ratios used are eta_j =
          logit(P[Y=j|Y>=j]) for j=1,...,M. If 'reverse' is 'TRUE',
          then eta_j = logit(P[Y=j+1|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}. The default value means none are
          modelled as intercept-only terms.

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

     There are a number of definitions for the _continuation ratio_ in
     the literature. To make life easier, in the 'VGAM' package, we use
     _continuation_ ratios (see 'cratio') and _stopping_ ratios. 
     Continuation ratios deal with quantities such as
     'logit(P[Y>j|Y>=j])'.

_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; see
     'ordered'.

_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.

     McCullagh, P. and Nelder, J. A. (1989) _Generalized Linear
     Models_, 2nd ed. London: Chapman & Hall.

     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:

     'cratio', 'acat', 'cumulative', 'multinomial', 'pneumo', 'logit',
     'probit', 'cloglog', 'cauchit'.

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

     data(pneumo)
     pneumo = transform(pneumo, let=log(exposure.time))
     (fit = vglm(cbind(normal,mild,severe) ~ let, sratio(parallel=TRUE), pneumo))
     coef(fit, matrix=TRUE)
     constraints(fit)
     predict(fit)
     predict(fit, untransform=TRUE)

