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What is SEM (Structural Equation Modeling)?

======================Stan Mulaik, 5 Apr 1995=========ssc Message-ID: <9504060004.AA00553@psy.skiles.gatech.edu> From: Stan Mulaik <smulaik@PSY.SKILES.GATECH.EDU> Subject: Structural Equation Modeling In answer to the question about what it is: Structural Equation Modeling is a linear model, expressed in matrix form as the following: Y = AY + GX + E where Y is a px1 random vector of endogenous variables (also known as dependent variables), X is a m x 1 random vector of exogenous variables, and E is a p x 1 random vector of disturbance or "error" variables. The matrix A is pxp, and by convention has zero elements on its principal diagonal. A contains the coefficients indicating how much unit change in some endogenous variables produces change in other endogenous variables. The model also provides for some of the Y's and some of the X's to be latent variables as in common factor analysis. The model is generally used to test substantive hypotheses involving causal relations of a linear nature. Researchers specify a priori certain parameters of the matrices A and G to overidentify the model. As long as the unspecified parameters are identified, these are estimated either by ML or GLS methods. It is assumed that the disturbance random variables in E are unrelated to the exogenous variables in X and to disturbance variables of other endogenous variables that are causal determinants of the endogenous variable to which the disturbance variable in question is assigned. Exogenous variables may be correlated. Because the covariance matrix among the manifest variables can be derived as functions of the A and G matrices, the model is generally tested by how well it reproduces the covariance matrix among the manifest variables. Stan Mulaik * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

What's the story about LISREL? Mulaik

=======================Stan Mulaik, 31 Oct 1994========ssc Message-ID: <9411010045.AA01655@psy.gatech.edu.noname> From: Stan Mulaik <smulaik@PSY.GATECH.EDU> Subject: SEM Jan Deleeuw has posted the following message: ----- I think there are basically two situations in which LISREL (or similar models) are not problematical. (a) There is very strong prior theory, which indicates that a particular SEM is appropriate, so that we only have to fit the coefficients. This happens, for instance, in mechanics and control theory. It also happens in Mendelian genetics. (b) We use the technique as an exploratory device. In that case it is dangerous to include a search over the space of models, because this is humongous and discrete. In exploratory cases I think the safe thing to do is stick with "global models" in which all arrows from block A to block B are there, or no arrows from block A to block B are there. This means that factor analysis, MIMIC, and state space models in their exploratory versions are useful exploratory devices. I also think LISREL cs are used differently in most cases. Researchers act as if they have firm prior information, while they don't. The "prejudices" (Kalman's term) are hidden in the model choice stage. Or researchers explore over the space of models, often without telling us about it, in which case they inflate their alpha levels by unknown amounts. The overall goodness-of-fit test obviously can never carry the burden of this very complicated model fitting ritual, and thus tends to be misleading. As long as LISREL research is presented as exploration, and the various decisions on the way to the final model are clearly documented, there is nothing wrong with it (although careful documentation will show that both the test of fit and the confidence intervals should not be taken seriously). If LISREL is used as a theory-generating device, it leads to the trouble I mentioned, because the theories that are generated in this way will be unstable under replication and of fleeting interest. --- Jan Jan de Leeuw; UCLA Statistics Program; UCLA Statistical Consulting --------- I think that is a fairly cautious, but firm statement about the problems of structural equation modeling. I don't have any major disagreements with it, although I am probably a stronger advocate of the technique. The thing I think psychologists have benefited from is thinking in terms of theories, constructs, and testing such with structural equation models. But Jan is right, confirmatory studies have to build on exploratory studies, or have to go through numerous iterations (as does most good science) to arrive at firm results. I'm not so sure that SEM works best with the single, one-shot dissertation study, especially if the student is unsure where to begin. Probably the worse people to use it are social psychologists who have no concept of the single variable latent construct. They think of independent variables like "subject's perception of situation threat", which obviously are not single-dimensional and yet try to model that as a single latent variable. They also don't work at developing sound measurement models before going on to test their structural models. Over a dozen years ago, Larry James, myself, and Jean Brett wrote a book "Causal Analysis: Assumptions, models and data" in which our major theme was considering experimental design considerations while implementing such models, just as they do in ANOVA studies. Some of that has gotten across to the I/O area, but other areas where this book was not marketed, did not get the message. By the way the book was put out by Sage publications. Stan Mulaik * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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