lecture12_s10 GM1 - General structural model Part 1 Power of testing mean-structure etc Psychology 588 Covariance structure and factor models Estimation

# lecture12_s10 GM1 - General structural model Part 1 Power...

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General structural model – Part 1: Power of testing, mean-structure, etc. Psychology 588: Covariance structure and factor models Mar 10, 2010 Estimation 2 Fitting functions ( F ML , F GLS , F ULS ) of a general SE model have the same forms as those for path modeling of observed variable only and CFA, but the implied covariance matrix is differently defined, e.g., Properties of the ML, GLS and ULS estimators hold essentially the same Given a converged solution, all estimates must be substantively sensible --- Exercise: fit the model explained in p. 334 to the political democracy data (with and without the equal-loading constraints in nested modeling approach); which are given in the data directory (poldemcov.xls) ( ) ( ) 1 ML ˆ ˆ log tr log F p q = + + Σ S Σ S Power of chi-square tests 3 Given a pair of nesting-nested models, we can set up H 0 and H a as follows: H 0 --- the constraints that make the only difference between the two models are correct, such that θ a = θ 0 , and θ b contains free parameters for both H 0 and H a H a --- The constraints are often θ a = 0 , though not necessary; it equally holds for constraints at nonzero constants If the nesting model (i.e., H a is true) has 0 df , the test is about goodness of fit of a hypothesized model [ ] a b , , = θ θ θ a 0 θ θ 