Structural equation modeling: Difference between revisions

Revision as of 04:29, 15 March 2006

Revision as of 17:52, 16 March 2006

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== Part 1: Introduction to SEM ==

SEM is an extension of the [[general linear model]] (GLM) that simultaneously estimates relationships between multiple independent and, dependent variables, in the case of a structural model and/or multiple observed and latent variables, in the case of confirmatory factor analysis. SEM is best applied to theory testing, as opposed to the more exploratory areas of theory development.

== Part 2: Basic concepts ==

* Basic steps in performing SEM analysis

# '''Model specification'''—Since SEM is a confirmatory technique, it is imperative that the model is specified correctly based on the type of analysis that the modeller is attempting to confirm. There are usually two main typesparts ofto modelsSEM: the ''structural model'' showing dependencies between latent and exogeneous variables, and the ''measurement model'' showing the relations between the latent variables and their indicators. Confirmatory [[factor analysis]] models, for example, only contain the measurement part; while linear regresion can be viewed as an SEM that only has the structural part. Specifying the model delineates relationships between variables that are thought to be related (and therefore want to be 'free' to vary) and those relationships between variables that already have an estimated relationship, which can be gathered from previous studies (these relationships are 'fixed' in the model).

# '''Estimation of free parameters'''—appropriating the best fitting model in SEM is an iterative process. Therefore, anparameter estimation is made comparing the actual variance/covariance matrices representing the relationships between variables and the estimated variance/covariance matrices of the best fitting model. This is obtained through numerical maximization of a ''fit criterion'' as provided by maximum likelihood, weighted least squares or asymptotically distribution free methods. This is best accomplished by using ana specialized SEM analysis program, such as AMOS, EQS, LISREL, orMplus, AMOSSAS PROC CALIS.

# '''Assessment of fit'''— Using an SEM analysis program, theone iterationscan compare the estimated matrices representing the relationships between variables in the model to the actual matrices. Individual factors within the model are also examined within the estimated model in order to see how well the proposed model fits the driving theory.

# '''Model modification'''— The model may need to be modified in order to maximize the fit, thereby estimating the most likely relationships between variables.

# '''Interpretation and communication'''—The model is then interpreted and claims about the constructs are made based on the best fitting model. Because SEM is limited to correlational data, caution should always be taken when making claims of causality unless further experimentation or time-ordered studies have been done.

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* Invariance

* Multiple group comparison

* Modeling growth

* Relations to other types of advanced models ([[multilevel models]]; IRT[[item response theory]] models)

* Alternative estimation and testing techniques

* Robust inference

* Interface with [[survey sampling|survey]] estimation

== See also ==

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*[http://www.gnu.org/software/pspp/pspp.html GNU PSPP] - a [[Free software|free software]] program designed as a replacement for SPSS

*[http://amosdevelopment.com/download/] student version of AMOS software for Structural Equation Modeling.

== References ==

;Books

* Bartholomew, D J, and Knott, M (1999) ''Latent Variable Models and Factor Analysis'' Kendall's Library of Statistics, vol. 7. Arnold publishers, ISBN 034069243X

* Bollen, K A (1989). ''Structural Equations with Latent Variables''. Wiley, ISBN 0471011711

* Bollen, K A, and Long, S J (1993) ''Testing Structural Equation Models''. SAGE Focus Edition, vol. 154, ISBN 0803945078

* Hoyle, R H (ed) (1995) ''Structural Equation Modeling: Concepts, Issues, and Applications''. SAGE, ISBN 0803953186

* Kaplan, D (2000) ''Structural Equation Modeling: Foundations and Extensions.'' SAGE, Advanced Quantitative Techniques in the Social Sciences series, vol. 10, ISBN 0761914072

[[Category:Statistics]]