

alias {base}                                 R Documentation

_F_i_n_d _A_l_i_a_s_e_s _(_D_e_p_e_n_d_e_n_c_i_e_s_) _i_n _a _M_o_d_e_l

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

     Find aliases (linearly dependent terms) in a linear
     model specified by a formula.

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

     alias(object, ...)
     alias.formula(object, data, ...)
     alias.lm(object, complete = TRUE, partial = FALSE, partial.pattern = FALSE)

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

  object: A fitted model object, for example from `lm' or
          `aov', or a formula for `alias.formula'.

    data: Optionally, a data frame to search for the objects
          in the formula.

complete: Should information on complete aliasing be
          included?

 partial: Should information on partial aliasing be
          included?

partial.pattern: Should partial aliasing be presented in a
          schematic way? If this is done, the results are
          presented in a more compact way, usually giving
          the deciles of the coefficients.

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

     Although the main method is for class `"lm"', `alias'
     is most useful for experimental designs and so is used
     with fits from `aov'.  Complete aliasing refers to
     effects in linear models that cannot be estimated inde-
     pendently of the terms which occur earlier in the model
     and so have their coefficients omitted from the fit.
     Partial aliasing refers to effects that can be esti-
     mated less precisely because of correlations induced by
     the design.

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

     A list (of `class "listof"') containing components

   Model: Description of the model; usually the formula.

Complete: A matrix with columns corresponding to effects
          that are linearly dependent on the rows; may be of
          class `"mtable"' which has its own `print' method.

 Partial: The correlations of the estimable effects, with a
          zero diagonal.

_N_o_t_e_:

     The aliasing pattern may depend on the contrasts in
     use: Helmert contrasts are probably most useful.

     The defaults are different from those in S.

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

     B.D. Ripley

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

     ## From Venables and Ripley (1997) p.210.
     N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
     P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
     K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
     yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
                62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
     npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
                       K=factor(K), yield=yield)

     ## The next line is optional (for fractions package which gives neater
     ## results.)
     has.VR <- require(MASS, quietly = TRUE)

     op <- options(contrasts=c("contr.helmert", "contr.poly"))
     npk.aov <- aov(yield ~ block + N*P*K, npk)
     alias(npk.aov)
     if(has.VR) detach(package:MASS)
     options(op)# reset

