

multilm(multilm)                             R Documentation

_M_u_l_i_v_a_r_i_a_t_e _L_i_n_e_a_r _M_o_d_e_l_s

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

     `multilm' fits a multivariate linear model und performs
     the Hotelling T^2 - Test for a given linear test prob-
     lem.

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

     multilm(formula, K, Z, data=list())

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

 formula: a symbolic description for the multivariate model
          to be tested

       K: a test matrix

       Z: a matrix for parameter restrictions

    data: an optional data frame containing the variables in
          the model.  By default the variables are taken
          from the environment which 'multilm' is called
          from

_D_e_t_a_i_l_s_:

     A multivariate linear model is a model of the form Y =
     X B + E, where Y is the matrix of responses, X is the
     design matrix, B is the matrix of coefficients and E a
     matrix of normally distributed errors. Parameter
     restrictions can be included by the Z matrix: Z B = 0
     (which has applications in MANOVA). `multilm' addition-
     ally calculates the Hotelling T^2-Test for the given
     test problem: H0: K B = 0. An approximation by Laeuter
     is used for the distribution of the T^2-statistic (and
     therefore for the p-value). T^2 is not very useful when
     the number of observations is limited but many vari-
     ables are included in the model. This problem is solved
     by the stabilized multivariate test procedures by
     Laeuter et. al. , which are available in `summary.mul-
     tilm'

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

     A object of class `multilm' containing the following
     components:

hotelstat: the T^2 test statistic

  hotelp: the pvalue of the T^2-test

coefficients: the matrix of estimated coefficients

   covar: the estimation of the covariance matrix

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

     Torsten Hothorn <hothorn@statistik.uni-dortmund.de>

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

     Ahrens, H.; Laeuter, J. (1981): Mehrdimensionale Vari-
     anzanalyse, Berlin

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

     `summary.multilm'

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

     # Edgar Anderson's famous iris data
     data(iris)
     # one-classification MANOVA, Y response matrix, X design matrix
     Y <- as.matrix(iris[,1:4]);
     x <- c(rep(1,50), rep(0,150), rep(1, 50), rep(0, 150), rep(1,50))
     X <- matrix(x, ncol=3)
     # restrictions: sum of effects equal zero
     Z <- c(0,1,1,1);
     # test for equal effects
     K <- cbind(0,diag(2),-1);
     # model (this method returns a multilm object)
     mod <- multilm(Y ~ X, K,Z);
     # output and stable tests
     summary(mod)            # Hotelling T^2: pvalue = 0

