The General LISREL Model

Ulf H. Olsson

Professor of statistics

Ulf H. Olsson

ESTIMATORS

• If the data are continuous and approximately follow a multivariate Normal distribution, then the Method of Maximum Likelihood is recommended.

• If the data are continuous and approximately do not follow a multivariate Normal distribution and the sample size is not large, then the Robust Maximum Likelihood Method is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample variances and covariances.

• If the data are ordinal, categorical or mixed, then the Diagonally Weighted Least Squares (DWLS) method for Polychoric correlation matrices is recommended. This method will require an estimate of the asymptotic covariance matrix of the sample correlations.

Ulf H. Olsson

Ordinal Variables

• In practice, observed or measured variables are often ordinal

• However, ordinality is often ignored and numbers such as 1,2,3, etc. representing ordered categories, are treated as continuous variables. But, this is incorrect!

Ulf H. Olsson

Making Numbers

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Loyalty

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Satisfaction

Ulf H. Olsson

Making Numbers-Econometric Model

2

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232221

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1

Ulf H. Olsson

Making Numbers-Psychometric Model

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Ulf H. Olsson

Making Numbers-Psychometric Model

9

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Ulf H. Olsson

Parameter Function

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')(')')('()()( 1

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BI

BIBIBI

Ulf H. Olsson

The Maximum Likelihood Estimator

tSStrFML log)()(log 1

Ulf H. Olsson

ML and RLS(NWLS)

k is the number of manifest variables.

kSStrSF log))(()(log))(,()1( 1

D is the duplication matrix (Magnus and Neudecker 1988) and is the ML estimate.

))(())()(('))'((2));(,()2(11

1

sDDsSF

Ulf H. Olsson

Drink and Drive case

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•See word file: Drinkdrivecaseuke38.doc

Ulf H. Olsson

Ulf H. Olsson

Making Numbers

1131211 SavingsLoanBranchonSatisfacti

221 onSatisfactiLoyalty

Loyalty

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Loan

Savings

Satisfaction

0.330.330.460.290.170.35 0.80

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