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The General Structural Equations model with latent variables

The General Structural Equations model with latent variables. by Willem E.Saris. Specification of a full SE model. A full SE model consists of three parts: a structural model a measurement model for the endogenous variables a measurement model for the exogenous variables

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The General Structural Equations model with latent variables

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  1. The General Structural Equations model with latent variables by Willem E.Saris

  2. Specification of a full SE model • A full SE model consists of three parts: • a structural model • a measurement model for the endogenous variables • a measurement model for the exogenous variables • This approach will be illustrated by an example college titel en nummer

  3. The structural model college titel en nummer

  4. The measurement of the endogenous variables college titel en nummer

  5. The Measurement model for the exogenous variables x1 • d1 Perception environmental damage x2 • d2 • d3 x3 Understanding politics x4 • d4 college titel en nummer

  6. A General Approach illustrated college titel en nummer

  7. The LISREL model college titel en nummer

  8. Decomposition of the full system • The covariance matrix of the observed variables is denoted by S. This matrix consists of three submatrices Syy Syx = Sxy ‘Sxx • Syy = Ly CLy’ + Qe • C = (I-B)-1(GFG’ +Y)(I-B)’-1 • Sxx =Lx FLx’ + Qd • Syx = Ly(I-B)-1GFLx’ • This result holds for all SE models !! college titel en nummer

  9. The decomposition of the covariance matrix in the parameters college titel en nummer

  10. Specific models of the full model • regression • recursive models • Non-recursive models • factor analysis • second order factor models • mimic models • panel models • Multiple groups models • latent growth models college titel en nummer

  11. Identification • If the measurement models are identified • and • the structural model are identified • then the full model is identified • Then the models can be estimated • If df> 0 the model can also be tested college titel en nummer

  12. Identification • Measurement models are identified • - if each latent variables has 3 indicators • - if each latent variables has two indicators but the latent variables are correlated • For the structural part of the model the identification rules of the econometric literature can be applied • A practical rule is: • If the standard errors of the parameters can be estimated then the model is identified college titel en nummer

  13. Estimation and testing of the full system • With respect to estimation nothing has been changed • Different estimators are available: ULS, ADF, ML • All three are consistent but they have different advantages and disadvantages as discussed before. • Testing also does not change but we will discuss it in more detail because it is essential and not so simple as presented so far. college titel en nummer

  14. SEM Approach • A model is specified with observed and latent variables • If the model is identified the parameters can be estimated including the effects between latent variables i.e. corrected for measurement error. • A test of the model can be performed if df>0 • Eventual misspecifications can be detected • Corrections in the models can be introduced college titel en nummer

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