pdLogChol-class             package:lme4             R Documentation

_C_l_a_s_s "_p_d_L_o_g_C_h_o_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 non-zero elements in the Cholesky
     decomposition.  The diagonal elements are represented by their
     logarithms in the first `q' positions of the parameter vector. 
     The strict upper triangle of the factor is in the last `q(q-1)/2'
     positions.

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

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

     `pdLogChol' 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:

     `_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.

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

     `_N_c_o_l': Object of class `"integer", from class "pdMat"', number of
          columns (and rows) in the positive-definite matrix.

     `_f_a_c_t_o_r': Object of class `"matrix", from class "pdMat"', a square
          root factor of the positive-definite matrix.

     `_l_o_g_D_e_t': Object of class `"numeric", from class "pdMat"' the
          logarithm of the absolute value of the determinant of the
          square root factor or, equivalently, half the logarithm of
          the determinant 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 = "pdLogChol", nlev = "numeric", value =
          "matrix")': update the `pdLogChol' object in the EM algorithm
          for a mixed-effects model.

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

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

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

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

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

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

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

     `pdMat-class'

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

     m1 <- pdLogChol(~ age)
     coef(m1) <- rnorm(3)
     print(m1)
     solve(m1)

