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From |
Dick Campbell <dcamp@uic.edu> |

To |
"statalist-hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
st: Structural equations, latent variables and path analysis |

Date |
Fri, 08 Apr 2005 13:43:17 -0500 |

A recent query on the list asked about software for structural equation

modeling. Among social scientists outside of economics,

the term "structural equation" has come to mean so many

things that it is virtually meaningless. Thus, when people ask

for structural equation modeling software it is necessary to

go through a sort of triage process to find out what they actually

want to do.

Here are several meanings of the term and brief comments on

what is available in Stata.

1) A sequence of regression equations involving directly

observed variables (as opposed to latent) arranged in a simple recursive

system (loosely "one way causation") estimable by OLS,

sometimes referred to, again loosely, as "path analysis." (Actually, path

analysis is more general, but I will leave that aside).

As noted, for models involving continuous outcome variables,

Phil Ender's Pathreg is an easy way to specify such a set of equations.

Most people who do analyses of this kind will also want to get estimates of

direct and indirect effects along with their standard errors (or at least they

should), however Pathreg will not do that and, so far as I know, no

other Stata package will. There are routines for doing so in most latent

variable packages (see below), however for recursive models the computations

can be done by hand, although computations of standard errors can get a bit tedious.

2) A system of equations of a non-recursive nature often involving

simultaneity among endogenous variables and requiring instrumental

variables or some other means of identifying the model.

In this case, and in case 1, the term "structural equation" in the

econometric literature is used in sharp distinction to "reduced form."

There are many Stata routines to deal with this situation, beginning with IVREG.

Findit "instrumental variables" is a good place to start. However, many people

who use the term "structural equation model" are not referring to this distinction.

3) Models, with latent variables, including confirmatory factor analysis,.

Unfortunately, in some areas of social science, the term "structural equation"

has come to refer to latent variable models which can be dealt with by programs

such as LISREL, MPLUS, EQS, AMOS and several others, all of which also deal

quite nicely with directly observed variables and most of which do effect decompositions.

Latent variable models can be recursive or non-recursive and thus will

sometimes involve reduced form and structural equations. It is important

to realize however, that the term "structural equation" has a very distinct

meaning in the econometric literature which has nothing to do with latent variables.

A more correct term would be SEMUV or Structural Equation Models

with Unmeasured Variables, however that term, like this note perhaps, borders on the pedantic.

Within Stata, GLLAMM will deal with a very broad class of latent variable models as

well as cases 1 and 2 for both continuous and categorical outcomes. I don't believe

that it does the kind of effect decomposition referred to above, although

that is a relatively minor issue. A routine for doing so would be a nice addition to the Stata tool kit.

A complete and rigorous discussion of the relationship between structural

equation models and latent variable models can be found in Skrondal and Rabe-Hesketh's .

book "Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural

Equation Models."

Richard T. Campbell

University of Illinois at Chicago

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**Follow-Ups**:**Re: st: Structural equations, latent variables and path analysis***From:*Stas Kolenikov <skolenik@gmail.com>

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