Performs multivariate analysis of variance and covariance (R.W. Payne & G.M. Arnold).

Options

Printed output required from the multivariate analysis of covariance (ssp, tests); default test

Printed output from the univariate analyses of variance of the y-variates (as for the ANOVA PRINT option); default *

Printed output from the univariate unadjusted analyses of variance of the y-variates (as for the ANOVA UPRINT option); default *

Printed output from the univariate analyses of variance of the covariates (as for the ANOVA CPRINT option); default *

Treatment formula for the analysis; if this is not set, the default is taken from the setting (which must already have been defined) by the TREATMENTSTRUCTURE directive

Block formula for the analysis; if this is not set, the default is taken from any existing setting specified by the BLOCKSTRUCTURE directive and if neither has been set the design is assumed to be unstratified (i.e. to have a single error term)

Covariates for the analysis; by default MANOVA uses those listed by a previous COVARIATE directive (if any)

Limit on the number of factors in a treatment term

Contains elements first for the treatment terms and then the covariate term (if any), allowing the LRV's to be saved from one of the analyses; if a term is estimated in more than one stratum, the LRV is taken from the lowest stratum in which it is estimated

Printing of probabilities for F statistics and Chi-square variables (no, yes); default no

Parameter

Y-variates for an analysis

Description

Procedure MANOVA performs multivariate analysis of variance or covariance. The data variates are specified by the Y parameter.

The model for the design is specified by options of the procedure. TREATMENTSTRUCTURE specifies a model formula to define the treatment terms in the analysis; if this is unset, MANOVA will use the model already defined by the TREATMENTSTRUCTURE directive, or will fail if that too has not been set. BLOCKSTRUCTURE defines the underlying structure of the design, and MANOVA will use the model (if any) previously defined by the BLOCKSTRUCTURE directive if this is not set; these can both be omitted if there is only one error term (i.e. if the design is unstratified). The COVARIATES option specifies any covariates; by default MANOVA will take those already listed (if any) by the COVARIATE directive. The FACTORIAL option can be used to set a limit on the number of factors in the terms generated from the treatment formula.

The LRV option allows a pointer to be saved containing an LRV structure for each treatment term. When covariates have been specified, the pointer will also contain a final LRV structure for the covariate term. If a term is estimated in more than one stratum, the LRV is taken from the stratum that occurs last in the BLOCKTERMS pointer. The structures in the LRV hold the canonical variate loadings, roots and trace for the respective term.

The other options control printed output. PRINT indicates the output required from the multivariate analysis of covariance, with settings ssp to print the sums of squares and products matrices, and tests to print the various test statistics (Wilks Lambda, with Chi square and F approximations, the Pillai-Bartlett trace, Roy's maximum root test and the Lawley-Hotelling trace). APRINT, UPRINT and CPRINT control output from the univariate analyses of each of the y-variates, corresponding to ANOVA options PRINT, UPRINT and CPRINT, respectively. FPROBABILITY controls whether or not probabilities are produced for F-ratios and for Chi-square variables in the analysis; by default these are omitted.

Options: PRINT, APRINT, UPRINT, CPRINT, TREATMENTSTRUCTURE, BLOCKSTRUCTURE, COVARIATES, FACTORIAL, LRV, FPROBABILITY.

Method

The relevant theory, with formulae and references for the test statistics, can be found in Chatfield & Collins (1986, Chapter 9). The procedure analyses the data variates by ANOVA first as y-variates, and then as covariates in order to obtain the SSP matrices. The SSP matrices are then adjusted for the covariates, using matrix manipulation in CALCULATE, and LRV decompositions are done, before the test statistics are calculated (again using CALCULATE).

Action with RESTRICT

If any of the y-variates is restricted, the analysis will involve only the units not excluded by the restriction.

Reference