1. LECTURE 13 PATH MODELING EPSY 640 Texas A&M University

2. Path Modeling Effects: –Direct effect –Indirect effect –Spurious effect –Unanalyzed effect

3. REVISING MODELS Classical regression approach –Forward: add variables according to improvement in R 2 for sample or population –Backward: start with all variables, remove those not contributing significantly to R 2 –Stepwise: use forward and backward together

4. REVISING MODELS SEM approach Model testing –improvement in fitting data Chi square test for model improvement (reduce model chi square significantly) Goodness of fit indices (based on chi square) –GFI, AGFI (proportional reduction in chi square) –NFI, CFI (model improvement, adjusted for df)

5. REVISING MODELS Changing paths in classical or SEM regression and path analysis –t-test for significance of regression coefficient (path coefficient)- test in unstandardized form –Lagrange Multiplier chi-square test that restricted path should not be zero –Wald chi square test that free path should be zero

6. REVISING MODELS t-test for significance of regression coefficient (path coefficient)- test in unstandardized form –coefficients are notoriously unstable in sample estimation –worse in forward or backward selections –different issue for sample-to-sample variation vs. sample-to-population variation

7. REVISING MODELS Purposes for regression determine interpretation of coefficients: –prediction: sets of coefficients are more stable than individual coefficients from one sample to the next:.5X +.3Y, may instead be better to assume next sample has sum of coefficients=.8 but that either one may not be close to.5 or.3

8. REVISING MODELS Purposes for regression determine interpretation of coefficients: –Theory-building: review of studies may provide distribution of coefficients (effect sizes), try to fit current research finding into the distribution –eg. Range of correlations between SES and IQ may be between -.1 and.6, mean of.33, SD=.15 –Did current result fit in the distribution?

9. REVISING MODELS OUTLIER ANALYSIS –Look at difference between predicted and actual score for each scores –Which differences are large? –Which of the predictor scores are most “discrepant” and causing the large difference in outcome? –Remove outlier and rerun analysis; does it change meaning or coefficients? –SPSS has such an analysis – VIF and CI indices

10. REVISING MODELS DROPPING PATHS THAT ARE NOT SIGNIFICANT –Drop one path only, then reanalyze, review results –Drop second path, reanalyze and review, especially possible inclusion of first path back in (modification indices, partial r’s) –Continue process with other candidate paths for deletion

13. REVISING MODELS COMPARING MODELS –R 2 improvement in subset regressions for path analysis [F-test with #paths dropped, df(error)] –Model fit analysis for entire path model- NFI, chi square change, etc. –Dropping paths increases MSerror, a tradeoff between increasing degrees of freedom for error (power) with reducing overall fit for model (loss of power): change of R 2 of chi-square per degree of freedom change

14. Venn Diagram for Model Change SSy SS for all effects but path being examined SS for path being examined SS added by path being examined

15. Biased Regression In some situations trade off biased estimate of regression coefficients for smaller standard errors Ridge regression is one approach: b* = b+  where  is a small amount –see if s e gets smaller as  is changed

16. MEDIATION VAR Y MEDIATES THE RELATIONSHIP BETWEEN X AND Z WHEN 1.X and Z are significantly related 2.X and Y are significantly related 3.Y and Z are significantly related 4.The relationship between X and Z is reduced (partial mediation) or zero (complete mediation) when Y partials the relationship X Y Z

17. X Y Z ex ez Partial correlation of X with Z partialling out Y

18. Z X Y r 2 XZ.Y

19. MEDIATION LOC SE DEP -.448.512 (.679) -.373

20. MEDIATION-Regressions LOC SE DEP -.448.512 -.373 Regression 1 Regression 2

21. GENERAL PATH MODELS LOC SE DEP -.448.512 -.373 Regression 1 Regression 2 ATYPIC ALITY Regression 3.400.357 R 2 =.481 R 2 =.574 R 2 =.200

22. GENERAL PATH MODELS LOC SE DEP -.448*.512* -.373* ATYPIC ALITY Regression 3.394.320* R 2 =.483 R 2 =.572 R 2 =.200 -.068 ns

23. GENERAL PATH MODELS LOC SE DEP -.448*.512* -.373* ATYPIC ALITY Regression 3.394.320* R 2 =.483 R 2 =.572 R 2 =.200 -.068 ns sex