1. Met 2212- Multivartate Statistics Ho-Testing OLS-regression LISREL IS GREEK TO ME The SEM model LISREL SOFTWARE Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson THE LISREL MODEL

3. Ulf H. Olsson THE LISREL MODEL Loyalty Branch Loan Savings Satisfaction

4. Ulf H. Olsson THE LISREL MODEL

5. Ulf H. Olsson THE LISREL MODEL (Factor Model)

6. Ulf H. Olsson THE LISREL MODEL (Factor Model)

7. Ulf H. Olsson THE LISREL MODEL

8. Ulf H. Olsson THE LISREL MODEL

9. Ulf H. Olsson THE LISREL MODEL

10. Ulf H. Olsson Greek Letters C A P / l o w e r N a m e & D e s c r i p t i o n A L P H A ( A L - f u h ) F i r s t l e t t e r o f t h e G r e e k a l p h a b e t. B E T A ( B A Y - t u h ) G A M M A ( G A M - u h ) D E L T A ( D E L - t u h ) E P S I L O N ( E P - s i l - o n ) T h e s e c o n d f o r m o f t h e l o w e r c a s e e p s i l o n i s u s e d a s t h e “ s e t m e m b e r s h i p ” s y m b o l. CAP / low er Name & Description ALPHA (AL-fuh) First letter of the Greek alphabet. BETA (BAY-tuh) GAMMA (GAM-uh) DELTA (DEL-tuh) EPSILON (EP-sil-on) The second form of the lower case epsilon is used as the “set membership” symbol.

11. Ulf H. Olsson Greek Letters ZETA (ZAY-tuh) ETA (AY-tuh) THETA (THAY-tuh) IOTA (eye-OH-tuh) KAPPA (KAP-uh)

12. Ulf H. Olsson Greek Letters LAMBDA (LAM-duh) MU (MYOO) NU (NOO) XI (KS-EYE) OMICRON (OM-i-KRON) Rarely used because it looks like an ‘o.’

13. Ulf H. Olsson Greek Letters PI (PIE) RHO (ROW) SIGMA (SIG-muh) TAU (TAU)

14. Ulf H. Olsson Greek Letters UPSILON (OOP-si-LON) PHI (FEE) The two versions of lower-case Phi are used interchangeably. CHI (K-EYE) PSI (SIGH) OMEGA (oh-MAY-guh) Last letter of the Greek alphabet.

15. Ulf H. Olsson Parameter Function

16. Ulf H. Olsson Multivariate Normal Distribution

17. Ulf H. Olsson The Maximum Likelihood Estimator

18. Measurement Error in Linear Multiple Regression Models Ulf H Olsson Professor Dep. Of Economics

19. Ulf H. Olsson The stadard linear multiple regression Model

20. Ulf H. Olsson Measurement Error/Errors-in-variables

21. Ulf H. Olsson The consequences of neglecting the measurent error

22. Ulf H. Olsson The consequences of neglecting the measurent error The probability limits of the two estimators when there is measurement error present: The disturbance term shares a stochastic term (V) with the regressor matrix => u is correlated with X and hence E(u|X)  0

23. Ulf H. Olsson The consequences of neglecting the measurent error Lack of orthogonality – crucial assumption underlying the use of OLS is violated !

24. Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

25. Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b

26. Ulf H. Olsson The consequences of neglecting the measurent error The inconsistency of b Bias towards zero (attenuation) for g=1 In multiple regression context things are less clear cut. Not all estimates are necessarilly biased towards zero, but there is an overall attenuation effect.

27. Ulf H. Olsson The consequences of neglecting the measurent error In the limit we find:

28. Ulf H. Olsson The consequences of neglecting the measurent error The estimator is biased upward

29. Ulf H. Olsson The consequences of neglecting the measurent error

30. Ulf H. Olsson The consequences of neglecting the measurent error