Structural equation modeling: Difference between revisions

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'''Structural equation modeling''' (SEM) is a [[statistical]] technique for building and testing [[statistical model]], which are often causal models. It is a hybrid technique that encompasses aspects of confirmatory [[factor analysis]], [[path analysis]] and [[regression]]., All of thesewhich can be seen as special cases of SEM.

SEM encourages a confirmatory, asrather opposed tothan exploratory, approachmodelling; tothus, modelling.it is Insuited otherto wordstheory testing, itrather isthan normaltheory todevelopment. start It usually starts with a [[hypothesis]], specify a model that reflectsrepresents it andas thena beginmodel, operationalisingoperationalises the constructs of interest with a measurement instrument and testtests the model. With an accepted theory or otherwise confirmed model, one can also use SEM inductively by specifying a model and using data to estimate the values of free parameters. Often the initial hypothesis requires adjustment in light of model evidence, but itSEM is rare to see SEMrarely used in a purely for exploration.

Among its strengths is the ability to model constructs as latent [[variable]]s which are not measured directly, but are estimated in the model from a number of measured variables assumed to 'tap into' the construct. This allows the modeller to explicitly capture unreliability of measurement in the model, in theory allowing the structural relations between latent variables to be accurately modelled.

Among its strengths is the ability to model constructs as latent [[latent variable]]s — variables which are not measured directly, but are estimated in the model from a number of measured variables which are assumed to 'tap into' the constructlatent variables. This allows the modeller to explicitly capture unreliability of measurement in the model, in theory allowing the structural relations between latent variables to be accurately modelled.

SEM encourages a confirmatory, as opposed to exploratory, approach to modelling. In other words, it is normal to start with a [[hypothesis]], specify a model that reflects it and then begin operationalising the constructs of interest with a measurement instrument and test the model. Often the initial hypothesis requires adjustment in light of model evidence, but it is rare to see SEM used in a purely for exploration.

SEM is an extension of the [[general linear model]] that simultaneously estimates relationships between multiple independent, dependent and latent variables. SEM is best applied to theory testing, as opposed to the more exploratory areas of theory development.

With an accepted theory or otherwise confirmed model, one can also use SEM inductively by specifying a model and using data to estimate the values of free parameters.

Alternatives to SEM for exploratory modeling include TETRAD and [[partial least squares]].

SEM is an extension of the [[general linear model]] that simultaneously estimates relationships between multiple independent, dependent and latent variables. SEM is best applied to theory testing, as opposed to the more exploratory areas of theory development.

== Steps in performing SEM analysis ==

TETRAD and [[partial least squares]] are alternatives to SEM for exploratory modeling.

=== BasicModel conceptsspecification ===

# '''Model specification'''—Since SEM is a confirmatory technique, it is imperative that the model ismust be specified correctly based on the type of analysis that the modeller is attempting to confirm. There are usually two main parts to SEM: 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, contain only the measurement part; while linear regression 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).

=== BasicEstimation stepsof infree performing SEM analysisparameters ===

# '''Estimation of free parameters'''—parameterParameter estimation is madedone comparing the actual variance/[[covariance matrix|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 a specialized SEM analysis program, such as AMOS, EQS, LISREL, Mplus, [http://www.vcu.edu/mx/ Mx], or SAS PROC CALIS.

This is best accomplished by using a specialized SEM analysis program, such as [http://www.spss.com/amos AMOS], EQS, LISREL, Mplus, [http://www.vcu.edu/mx/ Mx], or SAS PROC CALIS.

# '''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 parts to SEM: 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, contain only the measurement part; while linear regression 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'''—parameter 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 a specialized SEM analysis program, such as AMOS, EQS, LISREL, Mplus, [http://www.vcu.edu/mx/ Mx], or SAS PROC CALIS.

# '''Assessment of fit'''— Using an SEM analysis program, one can 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.

# '''Replication and revalidation''' — All model modifications should be replicated and revalidated before interpreting and communicating the results.

=== Advanced UsesAssessment of SEMfit ===

# '''Assessment of fit'''— Using an SEM analysis program, one can 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 ===

# '''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 ===

# '''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.

=== Replication and revalidation ===

# '''Replication and revalidation''' — All model modifications should be replicated and revalidated before interpreting and communicating the results.

== Advanced Uses ==

* Invariance

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== See also ==

* [[List of publications in statistics]]

* [[List of statistical topics]]

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== 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