1. 1 Comments Yutaka Kano Osaka University kano@hus.osaka-u.ac.jp

2. 2 Ultra-brief History Path Analysis by S. Wright Graphical MethodSEM Covariance selection Log-linear model Factor analysis

3. 3 Problems of Path Analysis 1.Difficulty presuming a causal model 2.No way of examination of appropriateness of the causal model considered 3.Vague relationship between causality and probability 4.Effect of (unobserved) third variables (confounding factors) X1X2 F

4. 4 Have Been Solved? SEM solves 2 GM appears to solve 1, 2 and 3 Both do not solve 4

5. 5 Similarity and Distinction GM –Can be used for exploratory purpose –Mainly manifest variables SEM –Confirmatory analysis –Latent variables

6. 6 How Does GM Treat? Mean structure Multiple populations Mean structure analysis in multiple populations

7. 7 Nonlinear? SEM has not fully developed tools for nonlinear effects GM looks to treat the nonlinear effects because its theory is derived under general probability functions not just under linear equations Intervention effect for nonlinear models

8. 8 Bayesian GM Utilize experiences based on expert judgment and past cases Minimize specification error of conditional distributions –May include –error for causal mechanism: linear or nonlinear –error for distributional assumption

9. 9 Robustness Study in SEM What if normality assumption is violated? Two cases –To what extent normal theory (NT) results remain correct –How one should infer if NT results are incorrect Consequences –NT is correct if latent factors are independent –Asymptotically distribution free method should be employed

10. 10 Future ? Path Analysis by S. Wright Graphical MethodSEM Covariance selection Log-linear model Factor analysis

11. 11 Bill Shipley(2000) Says “GM is an important development that could move current research in SEM into new territory” (page 639 in SEM)