The General LISREL MODEL Ulf H. Olsson Professor of Statistics.

The General LISREL MODEL

Ulf H. Olsson

Professor of Statistics

Ulf H. Olsson

Making Numbers

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Making Numbers-Econometric Model

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Ulf H. Olsson

Making Numbers-Psychometric Model

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Ulf H. Olsson

Making Numbers-Psychometric Model

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Ulf H. Olsson

Parameter Function

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Ulf H. Olsson

Making Numbers

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S: sample covariance

θ: parameter vector

σ(θ): model implied covariance

Ulf H. Olsson

Making Numbers

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Ulf H. Olsson

Making Numbers

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Ulf H. Olsson

Making Numbers

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Ulf H. Olsson

Making Numbers

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Ulf H. Olsson

Making Numbers

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Ulf H. Olsson

Making Significance

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Ulf H. Olsson

Making Numbers

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0.800.830.860.830.84

0.400.390.330.440.370.37

0.260.230.210.280.230.23

•Chi-sq.•1769.36• 925.78•1731.09• 839.83• 518.94• 582.91• df=182

Ulf H. Olsson

Multivariate Normal Distribution

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Ulf H. Olsson

The Maximum Likelihood Estimator

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Ulf H. Olsson

Making Significance

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Ulf H. Olsson

Making Significance (Sense)

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Ulf H. Olsson

Making Sense

If the model is correctly specified,different estimators shouldhave similar values asymptotically(White, 1994)

If the different estimators do not have similar values asymptotically, the model is misspecified

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1) Use at least two estimators 1 and 2; if they differ the model is misspecified;

2) Across-method variability can be used to assess what parts of the model, if any,are close to the true model??

Ulf H. Olsson

Making Sense

A strong theory will give precise predictions!

Ulf H. Olsson

Making sense is more important than making numbers, it is even more

important than making significance

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Ulf H. Olsson

Assignment

• 1) Evaluate the nine-psychological test model• 2) Estimate EX32A.Ls8• 3) Estimate Ex32B.ls8• 4) Estimate Ex56.Ls8