1. 1 Composites and Nonlinear Modeling data from Grace and Keeley (2006) Ecological Applications

2. 2 Bivariate relationship between total cover and richness How do we model the fit to the nonlinear line?

3. 3 A Simple Nonlinear Model

4. 4 A Simple Nonlinear Model - Results Note that these are standardized coefficients. What do they mean? Are the two main path coefficients significant contributors to the model?

5. 5 Amos Output p-values imply both paths contribute significantly. we can also test to see if the model fit is poor with paths omitted.

6. 6 Model Evaluation Chi-square increased by more than 3.84 when a single path was omitted, thus missing path deemed important to include.

7. 7 Using Composite to Summarize Nonlinear Effect A composite is created using a latent variable having a zero variance. Identification achieved by fixing one incoming path to 1.0. latent variable zero variance fixed path

8. 8 Nonlinear Model Results R-square consistent with path coef. standardized coefficient Test for nonlinearity performed prior to introduction of composite.

9. 9 What about when the nonlinear effect is endogenous?

10. 10 Endogenous Nonlinear Model Note that the polynomial term is treated as an exogenous variable.

11. 11 Endogenous Nonlinear Model Results

12. 12 Endogenous Nonlinear Model with Composite

13. 13 We can also use composites for other purposes. soil prop1 soil prop2 soil prop3 flooding frequency earthworm density Step 1 - test that all paths should be in model. soil prop1 soil prop2 soil prop3 flooding frequency earthworm density Step 2 - estimate collective effect using composite. soil effects e1 0 Now we can compare the collective effects of soil properties to the effects of flooding frequency on earthworm density.