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11 Jul 14
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SEM) is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions
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Structural equation models (SEM) allow both confirmatory and exploratory modeling, meaning they are suited to both theory testing and theory development
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Confirmatory modeling usually starts out with a hypothesis that gets represented in a causal model. The concepts used in the model must then be operationalized to allow testing of the relationships between the concepts in the model.
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When SEM is used purely for exploration, this is usually in the context of exploratory factor analysis as in psychometric design
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Among the strengths of SEM is the ability to construct latent variables: variables that are not measured directly, but are estimated in the model from several measured variables, each of which is predicted to 'tap into' the latent variables
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This allows the modeler to explicitly capture the unreliability of measurement in the model, which in theory allows the structural relations between latent variables to be accurately estimated
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In SEM, the qualitative causal assumptions are represented by the missing variables in each equation, as well as vanishing covariances among some error terms. These assumptions are testable in experimental studies and must be confirmed judgmentally in observational studies
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It is important to note that SEM is more general than regression. In particular, a variable can act as both independent and dependent variable.
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24 Mar 14
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20 Feb 14
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12 Apr 13
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27 Feb 13
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With an initial theory SEM can be used inductively by specifying a corresponding model and using data to estimate the values of free parameters.
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Among the strengths of SEM is the ability to construct latent variables: variables which are not measured directly, but are estimated in the model from several measured variables each of which is predicted to 'tap into' the latent variables. This allows the modeler to explicitly capture the unreliability of measurement in the model, which in theory allows the structural relations between latent variables to be accurately estimated. Factor analysis, path analysis and regression all represent special cases of SEM.
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In SEM, many models are equivalent in that they predict the same mean vector and covariance matrix. A "cleaned" model representation would be to model the mean and covariance matrix directly.
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In terms of path diagrams, CNM is the subset of SEMs that only have squares connected by double-headed edges.
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n a directed graph of the model, an exogenous variable is recognizable as any variable from which arrows only emanate, where the emanating arrows denote which variables that exogenous variable predicts. Any variable that regresses on another variable is defined to be an endogenous variable, even if other variables regress on it. In a directed graph, an endogenous variable is recognizable as any variable receiving an arrow.
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Two main components of models are distinguished in SEM: the structural model showing potential causal dependencies between endogenous and exogenous variables, and the measurement model showing the relations between latent variables and their indicators. Exploratory and Confirmatory factor analysis models, for example, contain only the measurement part, while path diagrams can be viewed as SEMs that contain only the structural part.
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A modeler will often specify a set of theoretically plausible models in order to assess whether the model proposed is the best of the set of possible models. Not only must the modeler account for the theoretical reasons for building the model as it is, but the modeler must also take into account the number of data points and the number of parameters that the model must estimate to identify the model.
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Not only must the modeler account for the theoretical reasons for building the model as it is, but the modeler must also take into account the number of data points and the number of parameters that the model must estimate to identify the model. An identified model is a model where a specific parameter value uniquely identifies the model, and no other equivalent formulation can be given by a different parameter value.
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The parameter is the value of interest, which might be a regression coefficient between the exogenous and the endogenous variable or the factor loading (regression coefficient between an indicator and its factor).
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Parameter estimation is done by comparing the actual covariance matrices representing the relationships between variables and the estimated covariance matrices of the best fitting model. This is obtained through numerical maximization of a fit criterion as provided by maximum likelihood estimation, weighted least squares or asymptotically distribution-free methods
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This is often accomplished by using a specialized SEM analysis program, of which several exist.
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Assessment of model and model fit
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- Akaike information criterion (AIC)
- A test of relative model fit: The preferred model is the one with the lowest AIC value.
- where k is the number of parameters in the statistical model, and L is the maximized value of the likelihood of the model.
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05 Sep 12
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16 Jun 12
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05 Mar 12
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21 Feb 12
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structural model showing potential causal dependencies between endogenous and exogenous variables
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measurement model showing the relations between latent variables and their indicators
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18 Nov 11
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19 Oct 11
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24 May 11
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28 Apr 11
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10 observations per indicator in setting a lower bound for the adequacy of sample sizes
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16 Aug 09
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ften the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability
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the model. The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data. With an accepted theory or otherwise confirmed model, SEM can also be used inductively by specifying the model and using data to estimate the values of free parameters. Often the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability t
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the model. The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data. With an accepted theory or otherwise confirmed model, SEM can also be used inductively by specifying the model and using data to estimate the values of free parameters. Often the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability t
-
Often the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability
-
Often the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability
-
Often the initial hypothesis requires adjustment in light of model evidence, but SEM is rarely used purely for exploration.
Among its strengths is the ability
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17 Jul 08
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24 Mar 08
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04 Feb 08
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16 Nov 07
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20 Aug 07
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