manova([Model] [,print:F or silent:T, coefs:F, pvals:T, fstats:T,\ byvar:T, sssp:F or T]), Model a CHARACTER scalar |

manova(Model) computes a MANOVA table of SS/SP (sums of squares and sums of products) matrices for the model in the CHARACTER variable Model. The response variable should be a matrix with rows as cases and columns the variables. Type 'help(models)' for information on how to specify Model. If the response is univariate (has only one column), manova() is equivalent to anova(). Unless 'marginal:T' is an argument, SS/SP matrices are computed sequentially (so called SAS Type I quantities). Normally, when each row of a SS/SP matrix will fit on a single line, all matrices are printed in their entirety. When a row would require more than one line, only the term names and the degrees of freedom are printed. This behavior can be modified by keywords 'sssp', 'byvar', 'fstats' and 'pvals'; see below. In any case the matrices are saved in the three-dimensional side effect array SS, with the first subscript indexing terms and with the first dimension labeled by TERMNAMES. manova(Model,weights:Wts) does a weighted analysis. Wts must be a REAL vector with Wts[i] >= 0 and nrows(Wts) = nrows(response). The results are the same as if the i-th row of the response and all X-variables (variates and dummy variables and their products), including the constant vector were multiplied by sqrt(Wts[i]) and a least squares fit (without an intercept) computed. manova() or manova(,weights:Wts) (no model supplied) uses the model used by the most recent GLM command such as manova(), anova(), or poisson(). See topic 'glm'. Side effect variables created are RESIDUALS, HII, DF, SS, DEPVNAME, TERMNAMES, and STRMODEL. When weights are specified, RESIDUALS = Response - Fitted and WTDRESIDUALS = sqrt(Wts)*RESIDUALS is an additional side effect vector. You should use WTDRESIDUALS rather than RESIDUALS in residual plots or other diagnostic procedures. SS is a 3-dimensional array such that SS[j,,] is the sum of squares and products matrix for term j. If the appropriate error matrix for the k-th term is SS[j,,], the eigenvalues needed for several standard tests (Wilks, Roy, Pillai, Hotelling generalized T-squared) may be computed by releigenvals(SS[j,,],SS[k,,]) or you can compute some test statistics directly, for example, Cmd> T2 <- dferror*trace(solve(SS[k,,],SS[j,,]) or Cmd> lambda <- det(SS[j,,])/det(SS[k,,]+SS[j,,]). Other Keywords Keyword phrase Default Meaning byvar:T F Computes a complete ANOVA table for each variable. The full SS/SP matrices are not printed although they are still available in array SS. sssp:T none Forces the printing of the full SS/SP matrices, even when each row would require more than one line. This option is ignored with any of fstats:T, pvals:T, or byvar:T. sssp:F Suppresses printing of the full SS/SP matrices, even if a row would fit on a single line. Only the term names and degrees of freedom are printed. See topic 'glm_keys' for information on keyword phrases 'print:F', 'silent:T', 'fstats:T', 'pvals:T', 'coefs:F' and 'marginal:T'. When byvar:T is an argument, options (not keywords) 'fstats' and 'pvals' have the same effect as with anova(). If byvar:T is not an argument, these options are ignored. See topics 'options' and 'glm_keys'. When byvar:T is not an argument, options 'fstats' and 'pvals' are ignored. If either 'fstats:T' or 'pvals:T' is an argument, univariate SS and MS are printed for each variable and term, together with F- statistics and/or P values . The information is essentially the same as with byvar:T except that all the statistics for a term are grouped together. The full SS/SP matrices are not printed but are available in array SS. Functions contrast(), coefs(), predtable(), and cellstats() work after a manova().

Gary Oehlert 2003-01-15