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Composites and Nonlinear Modeling

data from Grace and Keeley (2006) Ecological Applications

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02040

6080

100

0 100 200

Total Cover

Ric

hnes

s

Bivariate relationship betweentotal 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 coefficientssignificant contributors to the model?

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Amos Output

p-values imply bothpaths contributesignificantly.

we can also test to see if the modelfit is poor with paths omitted.

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Model Evaluation

Chi-square increased by more than 3.84when a single path was omitted, thusmissing path deemed important to include.

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Using Composite to Summarize Nonlinear Effect

A composite is created using a latent variablehaving a zero variance. Identification achievedby fixing one incoming path to 1.0.

latent variable

zero variancefixed path

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Nonlinear Model Results

R-square consistentwith path coef.

standardizedcoefficient

Test for nonlinearity performed prior to introduction of composite.

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What about when thenonlinear effect is

endogenous?

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Endogenous Nonlinear Model

Note that the polynomial term is treatedas 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.

soil prop1

soil prop2

soil prop3

floodingfrequency

earthwormdensity

Step 1 - test that all paths should be in model.

soil prop1

soil prop2

soil prop3

floodingfrequency

earthwormdensity

Step 2 - estimate collective effect using composite.

soileffects

e1

e1

0

Now we can compare the collective effectsof soil properties to the effects of floodingfrequency on earthworm density.