pdNatural-class             package:lme4             R Documentation

_C_l_a_s_s "_p_d_N_a_t_u_r_a_l", _p_o_s_i_t_i_v_e-_d_e_f_i_n_i_t_e _m_a_t_r_i_c_e_s

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

     A class of general, positive-definite symmetric matrices
     parameterized by the logarithm of the diagonal elements and
     Fisher's z transformation of the correlations.

_O_b_j_e_c_t_s _f_r_o_m _t_h_e _C_l_a_s_s:

     Objects can be created by calls of the form `new("pdNatural",
     ...)' or by the generic constructor function `pdNatural'.
     Frequently the constructor is given a formula only, creating an
     uninitialized `pdNatural' object which is later assigned a value.

     `pdNatural' objects are primarily used to represent the
     variance-covariance matrix or the precision matrix of
     random-effects terms in mixed-effects models.

_S_l_o_t_s:

     `_p_a_r_a_m': Object of class `"numeric", from class "pdMat"', a
          parameter vector of length [q(q+1)]/2 where q is the number
          of rows (and columns) in the positive-definite matrix.

     `_f_o_r_m': Object of class `"formula", from class "pdMat"', a formula
          for the object

     `_N_a_m_e_s': Object of class `"character", from class "pdMat"', names
          for the rows (and columns) of the positive-definite matrix.

_E_x_t_e_n_d_s:

     Class `"pdMat"', directly.

_M_e_t_h_o_d_s:

     _E_M_u_p_d_a_t_e<- `signature(x = "pdNatural", nlev = "numeric", value =
          "matrix")': update the `pdNatural' object in the EM algorithm
          for a mixed-effects model.

     _L_M_E_g_r_a_d_i_e_n_t `signature(x = "pdNatural", A = "matrix", nlev =
          "numeric")': evaluate the gradient of the log-likelihood in a
          linear mixed-effects model.

     _c_o_e_f `signature(object = "pdNatural")': extract the parameter.

     _c_o_e_f<- `signature(object = "pdNatural", value = "numeric")':
          assign the parameter.

     _c_o_e_r_c_e `signature(from = "pdNatural", to = "pdmatrix")': extract
          the positive-definite matrix represented by the object.

     _c_o_e_r_c_e `signature(from = "pdNatural", to = "pdfactor")': extract a
          square-root factor of the matrix represented by the object. 
          This factor has a `logDet' attribute giving the logarithm of
          its determinant.  In the case of `pdNatural' these are both
          scalars and the `logDet' attribute is the logarithm of the
          absolute value of the factor.

     _d_i_m `signature(x = "pdNatural")': the dimensions of the
          positive-definite matrix represented by the object. 

     _i_s_I_n_i_t_i_a_l_i_z_e_d `signature(object = "pdNatural")': a logical scalar
          indicating if the object is initialized. 

     _l_o_g_D_e_t `signature(object = "pdNatural", covariate = "missing")':
          the logarithm of the determinant of the factor of the
          positive-definite matrix represented by the object. 

     _p_d_g_r_a_d_i_e_n_t `signature(x = "pdNatural")': the gradient of the
          positive definite matrix with respect to the parameter
          vector.

     _s_o_l_v_e `signature(a = "pdNatural", b = "missing")': a `pdNatural'
          object representing the inverse of the positive-definite
          matrix represented by this object.

     _s_u_m_m_a_r_y `signature(object = "pdNatural")': summarize the object.

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

     `pdMat-class'

