Met 2212 Multivariate Statistics Path Analysis Ulf H

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

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

Path Analysis = Simultaneous equation Modeling Ulf H. Olsson

THE PATH MODEL x 1 x 2 y 1 y 2 x 3 Ulf H. Olsson

THE PATH MODEL Ulf H. Olsson

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

Simple School Career Model Ulf H. Olsson

Ulf H. Olsson

STATISTICAL SYMBOLS - NOTATION Ulf H. Olsson

STATISTICAL SYMBOLS - NOTATION Ulf H. Olsson

STATISTICAL SYMBOLS - NOTATION Ulf H. Olsson

True Process Theoretical Domain Empirical Domain 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) Ulf H. Olsson

Identification • Necessary but not sufficient: Ulf H. Olsson

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

Fit Function Ulf H. Olsson

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

Multivariate Normal Distribution Ulf H. Olsson

THE GLS Fit Function Ulf H. Olsson

STATISTICAL SYMBOLS - NOTATION Ulf H. Olsson