Suppose that a regression variable in a multivariate model affects two or more response variables. For example, suppose that
response variables y1
and y2
depend on a regression variable x
. This dependence can be categorized as one of two types:
In the more common case, the regression coefficient of x
for y1
and the regression coefficient of x
for y2
are different. The relationship can be described as follows:
In the SSM procedure you can specify this type of relationship in two equivalent ways:
You can specify the variable x
in the MODEL statement for y1
and specify the variable x_copy
(a copy of x
) in the MODEL statement for y2
as follows:
x_copy = x; /* create a copy of x */ model y1 = x ...; model y2 = x_copy ...;
You can specify the variable x
in MODEL statements for both y1
and y2
as follows:
model y1 = x ...; model y2 = x ...;
This specification avoids creating x_copy
.
Of these two alternate ways, the first is preferred because x
and x_copy
can then be unambiguously used in an EVAL statement to refer to the terms and , respectively.
In the less common case, y1
and y2
share a common regression coefficient.The relationship can be described as follows:
You can specify this type of relationship by placing the regression coefficient in the model state vector as follows:
state beta(1) T(I) A1(1) ; /* beta is a constant state */ comp xeffect = beta*(x) ; model y1 = xeffect ...; model y2 = xeffect ...;
Here the STATE statement defines beta
as a one-dimensional, time-invariant constant (because the transition matrix is identity, the disturbance covariance is 0
and the initial state is diffuse). Next, the COMP statement defines xeffect
as the product between beta
and the variable x
. Subsequently, both y1
and y2
use xeffect
in their respective MODEL statements.