# GRM Syntax -
Example 4: Testing Equality of Regression Coefficients

This example illustrates how custom hypotheses tests can be specified
via GRM
syntax. Note that these tests can also be requested (using an efficient
and convenient user-interface) from the Results dialog.

You can run this example with the example data file Exp.sta.
A multiple regression model (see also Example
1: Multiple Regression) is specified, and tests of custom hypotheses
are requested (via the Estimate
keyword). Specifically, the coefficients are used to form linear combinations
of parameter estimates, and these linear combinations are then tested
against zero. Thus the hypotheses in the Estimate
statements below specify that the differences between the parameter estimates
are equal to zero, and hence, that they are of equal magnitude. If these
hypotheses are rejected, then one can assume that the three variables
have differential effects on the dependent variable. Note that multiple
Estimate
statements are included, to perform separate tests for the differences
between all pairs of predictors.

GLM;

{ Dependent variable: }

DEPENDENT
= STRESS_R;

COVARIATE
= CORRECT1 CORRECT2 CORRECT3;

{ A main-effects (multiple regression) design
is specified. }

DESIGN
= CORRECT1 + CORRECT2 + CORRECT3;

{ The following statement is not necessary
(the default value for Intercept is Include);

it is added
here to clarify the number of parameters for the Estimate

statement. }

INTERCEPT
= INCLUDE;

{ The order and number of coefficients for
the custom hypothesis must

match the
parameters in the model. Because the intercept is included in

the multiple
regression, there are 4 parameters. The first Estimate
statement

specifies
the test of the hypothesis that the parameter estimates for all

covariates
are (simultaneously) the same (that the two independent pairwise

differences
between the parameter estimates are equal to zero).
Note that this

hypothesis
has 2 degrees of freedom. }

ESTIMATE
= 0 1 -1 0

0
1 0 -1;

{ The next Estimate
statement specifies the test of the hypothesis that

the parameter
estimates for covariates Correct1
and Correct2 are

identical.
Note that this hypothesis has 1 degree of freedom.}

ESTIMATE
= 0 1 -1 0;

{ The next Estimate
statement specifies the test of the hypothesis that

the parameter
estimates for covariates Correct1
and Correct3 are

identical.
}

ESTIMATE
= 0 1 0
-1;

{ The next Estimate
statement specifies the test of the hypothesis that

the parameter
estimates for covariates Correct2
and Correct3 are

identical.
}

ESTIMATE
= 0 0
1 -1;

The results spreadsheets for these custom hypotheses can be requested
from the Results
dialog.

For more examples, see GRM Syntax -
Examples.