If the MODEL statement includes more than one
dependent variable, you can perform multivariate analysis of variance
with the MANOVA statement. The test-options define which effects
while the detail-options specify how to execute
the tests and what results to display.
- MANOVA < test-options >< / detail-options > ;
When a MANOVA statement appears before the first
RUN statement, PROC ANOVA enters a multivariate mode
with respect to the handling of missing values;
in addition to observations with missing independent
variables, observations with any missing dependent variables are
excluded from the analysis.
If you want to use this mode of handling missing
values but do not need any multivariate analyses,
specify the MANOVA option in the PROC ANOVA statement.
You can specify the following options in the MANOVA statement
as test-options in order to define which multivariate tests
- H=effects | INTERCEPT | _ALL_
specifies effects in the preceding
model to use as hypothesis matrices.
for multivariate tests
For each SSCP matrix H associated with an effect, the H=
specification computes an analysis based on the characteristic roots
of E-1H, where E is the matrix associated
with the error effect. The characteristic roots and vectors are
displayed, along with the Hotelling-Lawley trace, Pillai's trace,
Wilks' criterion, and Roy's maximum root criterion with approximate
Use the keyword INTERCEPT to produce tests for the intercept.
To produce tests for all effects listed in the MODEL statement,
use the keyword _ALL_ in place of a list of effects.
For background and further details, see
the "Multivariate Analysis of Variance" section in Chapter 30, "The GLM Procedure."
specifies the error effect.
If you omit the E= specification, the ANOVA procedure uses the
error SSCP (residual) matrix from the analysis.
- M=equation,...,equation |
specifies a transformation matrix for the
dependent variables listed in the MODEL statement.
The equations in the M= specification are of the form
where the ci values are coefficients
for the various dependent-variables.
If the value of a given ci is 1, it may be omitted;
in other words 1 ×Y is the same as Y.
Equations should involve two or more dependent variables.
For sample syntax, see the "Examples" section.
Alternatively, you can input the transformation matrix
directly by entering the elements of the matrix with commas
separating the rows, and parentheses surrounding the matrix.
When this alternate form of input is used, the number of elements
in each row must equal the number of dependent variables.
Although these combinations actually represent the
columns of the M matrix, they are displayed by rows.
When you include an M= specification, the analysis
requested in the MANOVA statement is carried out
for the variables defined by the equations in the
specification, not the original dependent variables.
If you omit the M= option, the analysis is performed for the
original dependent variables in the MODEL statement.
If an M= specification is included without either
the MNAMES= or the PREFIX= option, the variables are
labeled MVAR1, MVAR2, and so forth by default.
For further information, see the section "Multivariate Analysis of Variance"
in Chapter 30, "The GLM Procedure."
provides names for the variables defined
by the equations in the M= specification.
Names in the list correspond to the M= equations or
the rows of the M matrix (as it is entered).
is an alternative means of identifying the
transformed variables defined by the M= specification.
For example, if you specify PREFIX=DIFF, the transformed
variables are labeled DIFF1, DIFF2, and so forth.
You can specify the following options in
the MANOVA statement after a slash as detail-options:
The following statements give several
examples of using a MANOVA statement.
produces a canonical analysis of the H and
E matrices (transformed by the M
matrix, if specified) instead of the default
display of characteristic roots and vectors.
requests that the transformation matrix in the
M= specification of the MANOVA statement be
orthonormalized by rows before the analysis.
displays the error SSCP matrix E.
If the E matrix is the error SSCP (residual) matrix
from the analysis, the partial correlations of the dependent
variables given the independent variables are also produced.
For example, the statement
manova / printe;
displays the error SSCP matrix and the partial correlation
matrix computed from the error SSCP matrix.
displays the hypothesis SSCP matrix H associated
with each effect specified by the H= specification.
produces analysis-of-variance tables for each dependent variable.
When no M matrix is specified, a table is produced for each
original dependent variable from the MODEL statement; with an
M matrix other than the identity, a table is produced
for each transformed variable defined by the M matrix.
class A B;
model Y1-Y5=A B(A);
manova h=A e=B(A) / printh printe;
manova h=B(A) / printe;
manova h=A e=B(A) m=Y1-Y2,Y2-Y3,Y3-Y4,Y4-Y5
manova h=A e=B(A) m=(1 -1 0 0 0,
0 1 -1 0 0,
0 0 1 -1 0,
0 0 0 1 -1) prefix=diff;
The first MANOVA statement specifies A as the
hypothesis effect and B(A) as the error effect.
As a result of the PRINTH option, the procedure displays the
hypothesis SSCP matrix associated with the A effect; and,
as a result of the PRINTE option, the procedure displays the
error SSCP matrix associated with the B(A) effect.
The second MANOVA statement specifies
B(A) as the hypothesis effect.
Since no error effect is specified, PROC ANOVA uses the error
SSCP matrix from the analysis as the E matrix.
The PRINTE option displays this E matrix.
Since the E matrix is the error SSCP matrix
from the analysis, the partial correlation matrix
computed from this matrix is also produced.
The third MANOVA statement requests the same analysis
as the first MANOVA statement, but the analysis is
carried out for variables transformed to be successive
differences between the original dependent variables.
The PREFIX=DIFF specification labels the transformed
variables as DIFF1, DIFF2, DIFF3, and DIFF4.
Finally, the fourth MANOVA statement has the
identical effect as the third, but it uses
an alternative form of the M= specification.
Instead of specifying a set of equations, the
fourth MANOVA statement specifies rows of a matrix
of coefficients for the five dependent variables.
As a second example of the use of the M= specification,
consider the following:
model dose1-dose4=group / nouni;
manova h = group
m = -3*dose1 - dose2 + dose3 + 3*dose4,
dose1 - dose2 - dose3 + dose4,
-dose1 + 3*dose2 - 3*dose3 + dose4
mnames = Linear Quadratic Cubic
The M= specification gives a transformation of the dependent
variables dose1 through dose4 into orthogonal polynomial
components, and the MNAMES= option labels the transformed
variables as LINEAR, QUADRATIC, and CUBIC, respectively.
Since the PRINTE option is specified and the default residual
matrix is used as an error term, the partial correlation matrix
of the orthogonal polynomial components is also produced.
For further information, see the "Multivariate Analysis of Variance" section in Chapter 30, "The GLM Procedure."
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.