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The GLM Procedure |

model y=x1 x2 x3;

To estimate the difference between the parameters for *x _{1}* and

you can use the following ESTIMATE statement:

estimate 'B1-B2' x1 1 x2 -1;

To predict *y* at *x _{1}*=1,

estimate 'B0+B1-2B3' intercept 1 x1 1 x3 -2;

Now consider models involving class variables such as

model y=A B A*B;

with the associated parameters:

The LS-mean for the first level of A is , where

You can estimate this with the following ESTIMATE statement:

estimate 'LS-mean(A1)' intercept 1 A 1 B 0.5 0.5 A*B 0.5 0.5;

Note in this statement that only one element of **L** is
specified following the A effect, even though A has three levels.
Whenever the list of constants following an effect
name is shorter than the effect's number of levels,
zeros are used as the remaining constants.
(If the list of constants is longer
than the number of levels for the effect, the extra
constants are ignored, and a warning message is displayed.)

To estimate the A linear effect in the preceding model,
assuming equally spaced levels for A,
you can use the following **L**:

The ESTIMATE statement for this **L** is written as

estimate 'A Linear' A -1 0 1;

If you do not specify the elements of **L** for
an effect that contains a specified effect, then
the elements of the specified effect are equally
distributed over the corresponding levels of the higher-order effect.
In addition, if you specify the intercept in an ESTIMATE or
CONTRAST statement, it is distributed over all classification
effects that are not contained by any other specified effect.
The distribution of lower-order coefficients to
higher-order effect coefficients follows the same
general rules as in the LSMEANS statement, and it is
similar to that used to construct Type IV tests.
In the previous example, the -1 associated with is divided by the number *n*_{1j} of parameters;
then each coefficient is set to -1/*n*_{1j}.
The 1 associated with is distributed among
the parameters in a similar fashion.
In the event that an unspecified effect contains several
specified effects, only that specified effect with the most
factors in common with the unspecified effect is used for
distribution of coefficients to the higher-order effect.

Numerous syntactical expressions for the ESTIMATE statement were considered, including many that involved specifying the effect and level information associated with each coefficient. For models involving higher-level effects, the requirement of specifying level information can lead to very bulky specifications. Consequently, the simpler form of the ESTIMATE statement described earlier was implemented.

The syntax of this ESTIMATE statement puts a burden on you to know a priori the order of the parameter list associated with each effect. You can use the ORDER= option in the PROC GLM statement to ensure that the levels of the classification effects are sorted appropriately.

**Note:**
If you use the ESTIMATE statement with unspecified effects,
use the E option to make sure that the actual
**L** constructed by the preceding rules is the one you intended.

where by default; you can change this with the SINGULAR= option. Continued fractions (like 1/3) should be specified to at least six decimal places, or the DIVISOR parameter should be used.

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