multilm               package: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 problem.

_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' additionally
     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
     variables are included in the model. This problem is solved by the
     stabilized multivariate test procedures by Laeuter et. al. , which
     are available in `summary.multilm'

_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 Varianzanalyse,
     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

