1. 1 Comparing SEM to the Univariate Model data from Grace and Keeley (2006) Ecological Applications

2. 2 A Graphical View of the Univariate Model

3. 3 Initial Univariate Results ns We might us a variety of criteria to decide which paths to retain. Here we use t-tests.

4. 4 Pruned Univariate Model

5. 5 What are the causal relationships? Structural Equation Meta-Model (SEMM) Species Richness Stand Age Fire Severity Plant Abundance Local Abiotic Conditions Within-plot Hetero- geneity Landscape Position Local Conditions Landscape Conditions Good time for thought experiments!

6. 6 Our Structural Equation Model

7. 7 SEM Results Are these results easier to interpret than those from the multiple regression?

8. 8 Some of the Amos Output here we see indications, in the form of p-values, that all parameters contribute significantly to the model.

9. 9 But wait, is the model sufficient? ask for residuals and modification indices, then rerun the model Model chi-square (p = 0.057) suggests that model is marginally adequate. But, we should perform some sensitivity tests by looking for indications of poor fit and evaluating some alternatives (to be safe).

10. 10 What do modification indices say? MI values greater than 4 are suggestive, but these values are only very approximate "hints" of whether modifications to model would lead to acceptance of additional pathways. All these MIs indicate that there may be a significant residual correlation between heterogeneity and total cover. We might want to see if there is a significant residual correlation between the two and, if so, to consider what process that would represent.

11. 11 What do residuals say? residuals ambiguous?.

12. 12 Try alternative model chi-square drops from 20.60 to 13.39, that's a difference of 7.21, indicating a significant improvement to the model.

13. 13 Now we are ready to consider the results! our unstandardized estimates our standardized estimates

14. 14 More results covariance between heterogeneity and cover is significant.

15. 15 And Still More Results R 2 for richness is pretty good, another indicator of model adequacy.