Sem Sch Mgmt & Budget
Sem Sch Mgmt & Budget EDLD 607
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This 3 page Class Notes was uploaded by Dee Bechtelar on Tuesday September 8, 2015. The Class Notes belongs to EDLD 607 at University of Oregon taught by Staff in Fall. Since its upload, it has received 55 views. For similar materials see /class/187161/edld-607-university-of-oregon in Educational Leadership at University of Oregon.
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Date Created: 09/08/15
Confirmatory Factor Analysis CFA Stevens Fall 1997 Model Speci cation The general CFA Model in SEM notation is XiAXEk65 where Xi a column vector of observed variables Ek ksi a column vector of latent variables AX lambda an i X k matrix of structural coefficients de ning the relations between the manifest X and latent E variables 66 thetadelta an i X i variancecovariance matrix of relations among the residual or error terms of X This general equation indicates that each manifest variable can be represented by a structural equation relating lambda ksi and thetadelta For example the Reisenzein 1986 SympathyAnger model can be represented by the path model on the following page Given that representation the following set of structural equations define the model X1 A11 1 6611 X All 1 6622 N X3 A31 1 6633 X4 A42 2 6644 X5 A52 2 6655 X6 A62 2 6666 Of course these equations can also be represented in matrix form which we will do in class An additional matrix is also necessary for model estimation the phi ltIgt matrix which is a variancecovariance matrix specifying the relationships among the latent E variables Mntlelm nrm t n Rnllm lolln there I Y f This isnsn y dune arhitrarilyhy nnenltwn methmls Methml the strnetnral enemeient Ax quotlnadingquot far one nfthe manilest variable is not estimated but is kl lnr all remaining lambdas and fertile variance nfthe relevant ksi Methml z the variances nfthe latent variables 5 are set to La Z mm 12 elements in the variancecovariance matrix where q a nlvariahlesin X X7Z 21 elements The numbernlparameters in the model ist 4 am 1 1 h h erm t Ix 39 13 parameters 39 waythe mmlel therelnre has21 r 13 l degreesnffn dnm 2 Model Estimation As described in the previous handout as long as the SEM model is overidentified iterative estimation procedures most often Maximum Likelihood are used to minimize the discrepancies between S the sample variancecovariance matrix and 26 the model implied estimate of the population variancecovariance matrix measured as F the tting function The CFA model can be used to attempt to reproduce S through the following equation note that now the phi matrix becomes part of the model 20 AXCDAX 05 This equation indicates that a variancecovariance matrix is formed through manipulation of the structural matrices implied by the specified CFA model This then provides a basis for evaluating goodnessof t GOF as in 72N1F
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