RMULTIVARIATE procedure

Performs multivariate linear regression with accumulated tests; synonym FITMULTIVARIATE (H. van der Voet).

Options

PRINT = string tokens	Controls printed output (model, summary, accumulated); default mode, summ, accu
RPRINT = string tokens	Controls printed output from the univariate regression analyses (model, deviance, summary, estimates, correlations, fittedvalues, accumulated, monitoring); default *
FACTORIAL = scalar	Limit for expansion of model terms; default 3
NOMESSAGE = string tokens	Which warning messages to suppress when fitting the complete model – messages are always suppressed when fitting models for individual tests (aliasing, marginality); default *
RESULTS = pointer	To save results from accumulated and summary tests in a pointer containing terms, degrees of freedom of terms, Wilks’ Lambda, Rao’s F-statistic, degrees of freedom for numerator and denominator of Rao’s F and P-value of Rao’s F

Parameter

TERMS = formula	List of explanatory variates and factors, or model formula

Description

RMULTIVARIATE calculates hierarchical tests for all terms in a multivariate linear regression model. These tests are based on Wilks’ Lambda. The use of RMULTIVARIATE must be preceded by a MODEL statement to define the response variables and, if required, a vector of weights and an offset. Generalized linear models are not allowed. Note that the FIT directive performs a regression analysis for each of the response variables in turn, whereas RMULTIVARIATE performs multivariate modelling and testing.

The TERMS parameter specifies the model terms to be assessed. The FACTORIAL option sets a limit on the number of factors and variates in each term, similarly to the FACTORIAL option of FIT; by default this is 3. Printed output from the multivariate analysis is controlled by the PRINT option: model gives a description of the model, summary prints test results for the full model, while accumulated gives accumulated test results for each term in the model formula. The RPRINT option controls output from univariate regressions of the individual variates, which are performed (by FIT) in order to calculate the multivariate analysis. The NOMESSAGE option can be used to suppress aliasing and marginality warning messages when fitting the full model.

The RESULTS option can be used to save both accumulated and summary test results in a pointer. This pointer contains a text structure saving the individual model terms and six variates saving the number of degrees of freedom associated with each term, Wilks’ Lambda, Rao’s F-statistic, degrees of freedom for numerator and denominator of Rao’s F-statistic and the calculated P-value. Directives RDISPLAY and RKEEP can be used subsequent to RMULTIVARIATE, to display further output and store results from the univariate regressions of each response variate.

Units with one or more missing values in any term are excluded from the analysis. This implies that successive calls of RMULTIVARIATE may give different test results if terms with missing values are dropped or added.

Options: PRINT, RPRINT, FACTORIAL, NOMESSAGE, RESULTS.

Parameter: TERMS.

Method

The implementation is straightforward using Genstat regression and the FSSPM directive. Terms in the multivariate linear model are tested by Rao’s F-approximation for Wilks’ Lambda (Rao 1973).

Action with RESTRICT

Any restriction applied to vectors used in the regression model will apply also to the results from RMULTIVARIATE.

Reference

Rao, C.R. (1973). Linear Statistical Inference and its Applications. Wiley, New York.

See also

Procedures: MANOVA, MVAOD.

Commands for: Multivariate and cluster analysis, Repeated measurements.

Example

CAPTION  'RMULTIVARIATE example',\ 
         !t('Tumour growth data from C. Chatfield & A.J. Collins (1986),',\ 
         'Introduction to Multivariate Analysis (revised edition),',\ 
         'pages 143 and 176.'); STYLE=meta,plain
FACTOR   [NVALUES=18; LEVELS=!(4,20,34)] temp
FACTOR   [NVALUES=18; LABELS=!T(Male,Female)] sex
GENERATE temp,sex,3
VARIATE  [NVALUES=18] initweight,finalweight,tumourweight
READ     initweight,finalweight,tumourweight
  18.15 16.51 0.24     18.68 19.5  0.32     19.54 19.84 0.20
  19.15 19.49 0.16     18.35 19.81 0.17     20.68 19.44 0.22
  21.27 23.30 0.33     19.57 22.30 0.45     20.15 18.95 0.35
  18.87 22.00 0.25     20.66 21.08 0.20     21.56 20.34 0.20
  20.74 16.69 0.31     20.02 19.26 0.41     17.20 15.90 0.28
  20.22 19.00 0.18     18.38 17.92 0.30     20.85 19.90 0.17  :
MODEL    finalweight,tumourweight
RMULTIVARIATE [RPRINT=accumulated] initweight + temp * sex