

_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

     alias(object, ...)

_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 coeffcients.

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

     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
     independently 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
     estimated 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

