loglinb3                package:VGAM                R Documentation

_L_o_g_l_i_n_e_a_r _M_o_d_e_l _f_o_r _T_h_r_e_e _B_i_n_a_r_y _R_e_s_p_o_n_s_e_s

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

     Fits a loglinear model to three binary responses.

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

     loglinb3(exchangeable = FALSE, zero = NULL)

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

exchangeable: Logical. If 'TRUE', the three marginal probabilities are
          constrained to be equal. 

    zero: Which linear/additive predictor is modelled as an intercept
          only? A 'NULL' means none. 

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

     The model is P(Y1=y1,Y2=y2,Y3=y3) =

 exp(u0 + u1*y1 + u2*y2 + u3*y3 + u12*y1*y2 + u13*y1*y3+ u23*y2*y3)

     where y1, y2 and y3 are 0 or 1, and the parameters are u1, u2, u3,
     u12, u13, u23.  The normalizing parameter u0 can be expressed as a
     function of the other parameters. Note that a third-order
     association parameter, u123 for the product y1*y2*y3, is assumed
     to be zero for this family function.

     The linear/additive predictors are (eta1,eta2,...,eta6) =
     (u1,u2,u3,u12,u13,u23).

_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'.

     When fitted, the 'fitted.values' slot of the object contains the
     eight joint probabilities, labelled as (Y1,Y2,Y3) = (0,0,0),
     (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1),
     respectively.

_N_o_t_e:

     The response must be a three-column matrix of ones and zeros only.
     Note that each of the 8 combinations of the multivariate response
     need to appear in the data set, therefore data sets will need to
     be large in order for this family function to work.

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

     Thomas W. Yee

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

     Yee, T. W. and Wild, C. J. (2001) Discussion to: ``Smoothing
     spline ANOVA for multivariate Bernoulli observations, with
     application to ophthalmology data (with discussion)'' by Gao, F.,
     Wahba, G., Klein, R., Klein, B. _Journal of the American
     Statistical Association_, *96*, 127-160.

     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:

     'loglinb2', 'hunua'.

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

     data(hunua)
     fit = vglm(cbind(cyadea,beitaw,kniexc) ~ altitude, loglinb3, data=hunua)
     coef(fit, mat=TRUE)
     fitted(fit)[1:4,]
     summary(fit)

