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

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