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Introduction to Structural Equations with Latent Variables |

The SYSLIN procedure in the SAS/ETS product can also fit certain kinds of path models and linear structural equation models. PROC CALIS differs from PROC SYSLIN in that PROC CALIS allows more generality in the use of latent variables in the models. Latent variables are unobserved, hypothetical variables, as distinct from manifest variables, which are the observed data. PROC SYSLIN allows at most one latent variable, the error term, in each equation. PROC CALIS allows several latent variables to appear in an equation -in fact, all the variables in an equation can be latent as long as there are other equations that relate the latent variables to manifest variables.

Both the CALIS and SYSLIN procedures enable you to specify
a model as a system of linear equations.
When there are several equations, a given variable
may be a dependent variable in one equation
and an independent variable in other equations.
Therefore, additional terminology is needed to describe
unambiguously the roles of variables in the system.
Variables with values that are determined jointly and simultaneously
by the system of equations are called *endogenous variables*.
Variables with values that are determined outside the system,
that is, in a manner separate from the process described
by the system of equations, are called exogenous variables.
The purpose of the system of equations is to explain
the variation of each endogenous variable in terms of
exogenous variables or other endogenous variables or both.
Refer to Loehlin (1987, p. 4) for further discussion
of endogenous and exogenous variables.
In the econometric literature, error and disturbance
terms are usually distinguished from exogenous variables,
but in systems with more than one latent variable
in an equation, the distinction is not always clear.

In PROC SYSLIN, endogenous variables are identified by the ENDOGENOUS statement. When you specify structural equations in PROC CALIS, endogenous variables are assumed to be those that appear on the left-hand sides of the equations; a given variable may appear on the left-hand side of at most one equation.

PROC SYSLIN provides many methods of estimation, some of which are applicable only in special cases. For example, ordinary least-squares estimates are suitable in certain kinds of systems but may be statistically biased and inconsistent in other kinds. PROC CALIS provides three methods of estimation that can be used with most models. Both the CALIS and SYSLIN procedures can do maximum likelihood estimation, which PROC CALIS calls ML and PROC SYSLIN calls FIML. PROC SYSLIN can be much faster than PROC CALIS in those special cases for which it provides computationally efficient estimation methods. However, PROC CALIS has a variety of sophisticated algorithms for maximum likelihood estimation that may be much faster than FIML in PROC SYSLIN.

PROC CALIS can impose a wider variety of constraints on the parameters, including nonlinear constraints, than can PROC SYSLIN. For example, PROC CALIS can constrain error variances or covariances to equal specified constants, or it can constrain two error variances to have a specified ratio.

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