gam.side                package:mgcv                R Documentation

_I_d_e_n_t_i_f_i_a_b_i_l_i_t_y _s_i_d_e _c_o_n_d_i_t_i_o_n_s _f_o_r _a _G_A_M

_D_e_s_c_r_i_p_t_i_o_n:

     GAM formulae with repeated variables only correspond to
     identifiable models given some side conditions. This routine works
      out appropriate side conditions, based on zeroing redundant
     parameters. It is called from 'gam.setup' and is not intended to
     be called by users. 

     The method identifies nested and repeated variables by their
     names, but evaluates what constraints to impose, numerically.
     Constraints are always applied to smooths of more variables in
     preference to smooths of fewer variables. The numerical approach
     allows appropriate constraints to be applied to models constructed
     using any smooths, including user defined smooths.

_U_s_a_g_e:

     gam.side(sm,tol=.Machine$double.eps^.5)

_A_r_g_u_m_e_n_t_s:

      sm: A list of smooth objects as returned by 'smooth.construct'.

     tol: The tolernce to use when assessing linear dependence of
          smooths.

_D_e_t_a_i_l_s:

     Models such as  'y~s(x)+s(z)+s(x,z)' can be estimated by 'gam',
     but require identifiability constraints to be applied, to make
     them identifiable. This routine does this, effectively setting
     redundant parameters to zero. When the redundancy is between
     smooths of lower and higher numbers of variables, the constraint
     is always applied to the smooth of the higher number of variables. 

     Dependent smooths are identified symbolically, but which
     constraints are  needed to ensure identifiability of these smooths
     is determined numerically, using 'fixDependence'. This makes the
     routine rather general, and not dependent on any particular basis.

_V_a_l_u_e:

     A list of smooths, with model matrices and penalty matrices
     adjusted to automatically impose the required constraints. Any
     smooth that has been modified will have an attribute
     '"del.index"', listing the columns of its model matrix that were
     deleted. This index is used in the creation of prediction matrices
     for the term.

_A_u_t_h_o_r(_s):

     Simon N. Wood simon.wood@r-project.org

_E_x_a_m_p_l_e_s:

     set.seed(0)
     n<-400
     sig2<-4
     x0 <- runif(n, 0, 1)
     x1 <- runif(n, 0, 1)
     x2 <- runif(n, 0, 1)
     pi <- asin(1) * 2
     f <- 2 * sin(pi * x0)
     f <- f + exp(2 * x1) - 3.75887
     f <- f + 0.2 * x2^11 * (10 * (1 - x2))^6 + 10 * (10 * x2)^3 * (1 - x2)^10 - 1.396
     e <- rnorm(n, 0, sqrt(abs(sig2)))
     y <- f + e
     b<-gam(y~s(x0)+s(x1)+s(x0,x1)+s(x2))
     plot(b,pages=1)
     test1<-function(x,z,sx=0.3,sz=0.4)  
     { (pi**sx*sz)*(1.2*exp(-(x-0.2)^2/sx^2-(z-0.3)^2/sz^2)+
       0.8*exp(-(x-0.7)^2/sx^2-(z-0.8)^2/sz^2))
     }
     n<-500
     old.par<-par(mfrow=c(2,2))
     x<-runif(n);z<-runif(n);
     y<-test1(x,z)+rnorm(n)*0.1
     ## a fully nested tensor product example
     b<-gam(y~s(x,bs="cr",k=6)+s(z,bs="cr",k=6)+te(x,z,k=6))
     plot(b)
     par(old.par)
     rm(list=c("f","x0","x1","x2","x","z","y","b","test1","n","sig2","pi","e"))

