

pdSymm(nlme)                                 R Documentation

_G_e_n_e_r_a_l _P_o_s_i_t_i_v_e_-_D_e_f_i_n_i_t_e _M_a_t_r_i_x

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

     This function is a constructor for the `pdSymm' class,
     representing a general positive-definite matrix. If the
     matrix associated with `object' is of dimension n, it
     is represented by n*(n+1)/2 unrestricted parameters,
     using the matrix-logarithm parametrization described in
     Pinheiro and Bates (1996). When `value' is
     `numeric(0)', an uninitialized `pdMat' object, a one-
     sided formula, or a vector of character strings,
     `object' is returned as an uninitialized `pdSymm'
     object (with just some of its attributes and its class
     defined) and needs to have its coefficients assigned
     later, generally using the `coef' or `matrix' replace-
     ment functions. If `value' is an initialized `pdMat'
     object, `object' will be constructed from
     `as.matrix(value)'. Finally, if `value' is a numeric
     vector, it is assumed to represent the unrestricted
     coefficients of the matrix-logarithm parametrization of
     the underlying positive-definite matrix.

_U_s_a_g_e_:

     pdSymm(value, form, nam, data)

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

   value: an optional initialization value, which can be any
          of the following: a `pdMat' object, a positive-
          definite matrix, a one-sided linear formula (with
          variables separated by `+'), a vector of character
          strings, or a numeric vector. Defaults to
          `numeric(0)', corresponding to an uninitialized
          object.

    form: an optional one-sided linear formula specifying
          the row/column names for the matrix represented by
          `object'. Because factors may be present in
          `form', the formula needs to be evaluated on a
          data.frame to resolve the names it defines. This
          argument is ignored when `value' is a one-sided
          formula. Defaults to `NULL'.

     nam: an optional vector of character strings specifying
          the row/column names for the matrix represented by
          object. It must have length equal to the dimension
          of the underlying positive-definite matrix and
          unreplicated elements. This argument is ignored
          when `value' is a vector of character strings.
          Defaults to `NULL'.

    data: an optional data frame in which to evaluate the
          variables named in `value' and `form'. It is used
          to obtain the levels for `factors', which affect
          the dimensions and the row/column names of the
          underlying matrix. If `NULL', no attempt is made
          to obtain information on `factors' appearing in
          the formulas. Defaults to the parent frame from
          which the function was called.

_V_a_l_u_e_:

     a `pdSymm' object representing a general positive-defi-
     nite matrix, also inheriting from class `pdMat'.

_A_u_t_h_o_r_(_s_)_:

     Jose Pinheiro and Douglas Bates

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

     Pinheiro, J.C. and Bates., D.M.  (1996) "Unconstrained
     Parametrizations for Variance-Covariance Matrices",
     Statistics and Computing, 6, 289-296.

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

     `as.matrix.pdMat', `coef.pdMat', `matrix<-.pdMat'

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

     library(nlme)
     pd1 <- pdSymm(diag(1:3), nam = c("A","B","C"))
     pd1

