1. Met 2212 Multivariate Statistics Path Analysis Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson Path Analysis = Simultaneous equation Modeling System of regression equations

3. Ulf H. Olsson Path Analysis = Simultaneous equation Modeling

4. Ulf H. Olsson THE PATH MODEL y2 x1 x2 x3 y1

5. Ulf H. Olsson THE PATH MODEL

6. Ulf H. Olsson Simple School Career Model Ch. Of school Scholastic Achievement Q of elementary sch SES

7. Ulf H. Olsson Simple School Career Model

8. Ulf H. Olsson

9. STATISTICAL SYMBOLS - NOTATION

10. Ulf H. Olsson STATISTICAL SYMBOLS - NOTATION

11. Ulf H. Olsson STATISTICAL SYMBOLS - NOTATION

12. Ulf H. Olsson True Process Theoretical Domain Empirical Domain

13. Ulf H. Olsson Identification The parameter vector contains all the unknown elements The model is idenfied if the all the ”free” parameters in the model can uniquely be determined from the data (sample)

14. Ulf H. Olsson Identification Necessary but not sufficient:

15. Ulf H. Olsson Estimation of the Model parameters Assuming that the parameters are identified

16. Ulf H. Olsson Fit Function

17. Ulf H. Olsson THE ML Fit Function k is the number of manifest variables (k=p+q).

18. Ulf H. Olsson Multivariate Normal Distribution

19. Ulf H. Olsson THE GLS Fit Function

20. Ulf H. Olsson STATISTICAL SYMBOLS - NOTATION