pdTens                 package:mgcv                 R Documentation

_F_u_n_c_t_i_o_n_s _i_m_p_l_e_m_e_n_t_i_n_g _a _p_d_M_a_t _c_l_a_s_s _f_o_r _t_e_n_s_o_r _p_r_o_d_u_c_t _s_m_o_o_t_h_s

_D_e_s_c_r_i_p_t_i_o_n:

     This set of functions implements an 'nlme' library 'pdMat' class
     to allow tensor product smooths to be estimated by 'lme' as called
     by 'gamm'. Tensor product smooths have a penalty matrix made up of
     a weighted sum of penalty matrices, where the weights are the
     smoothing  parameters. In the mixed model formulation the penalty
     matrix is the inverse of the covariance matrix for  the random
     effects of a term, and the smoothing parameters (times a half) are
     variance parameters to be estimated.  It's not possible to
     transform the problem to make the required random effects
     covariance matrix look like one of the standard  'pdMat' classes:
     hence the need for the 'pdTens' class. A 'notLog2'
     parameterization ensures that  the parameters are positive. 

     These functions ('pdTens', 'pdConstruct.pdTens',
     'pdFactor.pdTens', 'pdMatrix.pdTens', 'coef.pdTens' and
     'summary.pdTens') would not normally be called directly.

_U_s_a_g_e:

     pdTens(value = numeric(0), form = NULL, 
            nam = NULL, data = sys.frame(sys.parent()))

_A_r_g_u_m_e_n_t_s:

   value: Initialization values for parameters. Not normally used.

    form: A one sided formula specifying the random effects structure.
          The formula should have an attribute 'S' which is a list of
          the penalty matrices the weighted sum of which gives the
          inverse of the  covariance matrix for these random effects.

     nam: a names argument, not normally used with this class.

    data: data frame in which to evaluate formula.

_D_e_t_a_i_l_s:

     If using this class directly note that it is worthwhile scaling
     the 'S' matrices to be of `moderate size', for example by dividing
     each matrix by its largest singular value: this avoids problems
     with 'lme' defaults ('smooth.construct.tensor.smooth.spec' does
     this automatically).  

     This appears to be the minimum set of functions required to
     implement a new 'pdMat' class. 

     Note that while the 'pdFactor' and 'pdMatrix' functions return the
     inverse of the scaled random  effect covariance matrix or its
     factor, the 'pdConstruct' function is sometimes initialised with
     estimates of the scaled covariance matrix, and sometimes
     intialized with its inverse.

_V_a_l_u_e:

     A class 'pdTens' object, or its coefficients or the matrix it
     represents or the factor of  that matrix. 'pdFactor' returns the
     factor as a vector (packed column-wise) ('pdMatrix' always returns
     a matrix).

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     Pinheiro J.C. and Bates, D.M. (2000) Mixed effects Models in S and
     S-PLUS. Springer

     The 'nlme' source code.

     <URL: http://www.maths.bath.ac.uk/~sw283/>

_S_e_e _A_l_s_o:

     'te'  'gamm'

_E_x_a_m_p_l_e_s:

     # see gamm