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# 10 together the structural model and the measurement

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10) Together, the structural model and the measurement model form the entire structural equation model . This model includes everything that has been measured, observed, or otherwise manipulated in the set of variables examined. 11) A recursive structural equation model is a model in which causation is directed in one single direction. A nonrecursive structural equation model has causation which flows in both directions at some parts of the model. SEM can conceptually be used to answer any research question involving the indirect or direct observation of one or more independent variables or one or more dependent variables. However, the primary goal of SEM is to determine and validify a proposed causal process and/or model. Therefore, SEM is a confirmatory technique. Like any other test or model, we have a sample and want to say something about the population that comprises the sample. We have a covariance

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237 matrix to serve as our dataset, which is based on the sample of collected measurements. The empirical question of SEM is therefore whether the proposed model produces a population covariance matrix that is consistent with the sample covariance matrix. Because one must specify a priori a model that will undergo validation testing, there are many questions SEM can answer. SEM can tell you how if your model is adequate or not. Parameters are estimated and compared with the sample covariance matrix. Goodness of fit statistics can be calculated that will tell you whether your model is appropriate or needs further revision. SEM can also be used to compare multiple theories that are specified a priori . SEM can tell you the amount of variance in the dependent variables (DVs) both manifest and latent DVs is accounted for by the IVs. It can also tell you the reliability of each measured variables. And, as previously mentioned, SEM allows you to examine mediation and moderation, which can include indirect effects. SEM can also tell you about group differences. You can fit separate structural equation models for different groups and compare results. In addition, you can include both random and fixed effects in your models and thus include hierarchical modeling techniques in your analyses. 23.3.2. LIMITATIONS AND ASSUMPTIONS REGARDING SEM Because SEM is a confirmatory technique, you must plan accordingly. You must specify a full model a priori and test that model based on the sample and variables included in your measurements. You must know the number of parameters you need to estimate including covariances, path coefficients, and variances. You must know all relationships you want to specify in the model. Then, and only then, can you begin your analyses. Because SEM has the ability to model complex relationships between multivariate data, sample size is an important (but unfortunately underemphasized) issue. Two popular assumptions are that you need more than 200 observations, or at least 50 more than 8 times the number of variables in the model. A larger sample size is always desired for SEM.
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• Spring '12
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