Composites and Nonlinear Modeling

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Composites and Nonlinear Modeling
data from Grace and Keeley (2006) Ecological
Applications
2
Bivariate relationship between total cover and
richness
How do we model the fit to the nonlinear line?
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A Simple Nonlinear Model
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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?
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Amos Output
p-values imply both paths contribute significantly
.
we can also test to see if the model fit is poor
with paths omitted.
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Model Evaluation
Chi-square increased by more than 3.84 when a
single path was omitted, thus missing path deemed
important to include.
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Using Composite to Summarize Nonlinear Effect
fixed path
zero variance
latent variable
A composite is created using a latent
variable having a zero variance. Identification
achieved by fixing one incoming path to 1.0.
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Nonlinear Model Results
standardized coefficient
R-square consistent with path coef.
Test for nonlinearity performed prior to
introduction of composite.
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What about when the nonlinear effect is
endogenous?
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Endogenous Nonlinear Model
Note that the polynomial term is treated as an
exogenous variable.
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Endogenous Nonlinear Model Results
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Endogenous Nonlinear Model with Composite
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We can also use composites for other purposes.
Step 1 - test that all paths should be in model.
soil prop1
soil prop2
earthworm density
e1
soil prop3
flooding frequency
Step 2 - estimate collective effect using
composite.
soil prop1
0
soil effects
soil prop2
earthworm density
e1
soil prop3
Now we can compare the collective effects of soil
properties to the effects of flooding frequency
on earthworm density.
flooding frequency