constraints               package:VGAM               R Documentation

_C_o_n_s_t_r_a_i_n_t _M_a_t_r_i_c_e_s

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

     Returns the _constraint matrices_ of objects in the 'VGAM'
     package.

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

     constraints(object, ...)

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

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

     ...: Other possible arguments. 

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

     Constraint matrices describe the relationship of
     coefficients/component functions of a particular explanatory
     variable between the linear/additive predictors in VGLM/VGAM
     models. For example, they may be all different (constraint matrix
     is the identity matrix) or all the same (constraint matrix has one
     column and has unit values).

     VGLMs and VGAMs have constraint matrices which are _known_. The
     class of RR-VGLMs have constraint matrices which are _unknown_ and
     are to be estimated.

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

     This extractor function returns a list comprising of constraint
     matrices-one for each column of the LM model matrix, and in that
     order. The list is labelled with the variable names. Each
     constraint matrix has M rows, where M is the number of
     linear/additive predictors, and whose rank is equal to the number
     of columns. A model with no constraints at all has an order M
     identity matrix as each variable's constraint matrix.

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

     The 'xij' argument changes things, and this has not been fully
     resolved yet.

_N_o_t_e:

     In all 'VGAM' family functions 'zero=NULL' means none of the
     linear/additive predictors are modelled as intercepts-only. Other
     arguments found in certain 'VGAM' family functions which affect
     constraint matrices include 'parallel' and 'exchangeable'.

     The 'constraints' argument in 'vglm' and 'vgam' allows constraint
     matrices to be inputted. If so, then 'constraints(fit)' should
     return the same as the input.

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

     T. W. Yee

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

     Yee, T. W. and Wild, C. J. (1996) Vector generalized additive
     models. _Journal of the Royal Statistical Society, Series B,
     Methodological_, *58*, 481-493.

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

     <URL: http://www.stat.auckland.ac.nz/~yee> contains additional
     information.

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

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

     Arguments such as 'zero' and 'parallel' found in many 'VGAM'
     family functions are a way of creating/modifying constraint
     matrices conveniently, e.g., see 'zero'.

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

     # Fit the proportional odds model
     data(pneumo)
     pneumo = transform(pneumo, let=log(exposure.time))
     fit = vglm(cbind(normal, mild, severe) ~ let,
                cumulative(parallel=TRUE, reverse=TRUE), pneumo)
     fit
     coef(fit, matrix=TRUE)
     constraints(fit)  # Parallel assumption results in this



     # Fit a rank-1 stereotype (RR-multinomial logit) model 
     data(car.all)
     fit = rrvglm(Country ~ Width + Height + HP, multinomial, car.all, Rank=1)
     constraints(fit) # All except the first are the A matrix 

