1

Comparing SEM to the Univariate Model

data from Grace and Keeley (2006) Ecological Applications

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A Graphical View of the Univariate Model

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Initial Univariate Results

ns

ns

We might us a variety of criteria to decidewhich paths to retain. Here we use t-tests.

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Pruned Univariate Model

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What are the causal relationships?Structural Equation Meta-Model

(SEMM)

SpeciesRichness

StandAge

FireSeverity

PlantAbundance

LocalAbiotic

Conditions

Within-plotHetero-geneity

LandscapePosition

Local ConditionsLandscape Conditions

Good time for thought experiments!

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Our Structural Equation Model

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SEM Results

Are these results easier to interpret thanthose from the multiple regression?

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Some of the Amos Output

here we see indications,in the form of p-values,that all parameterscontribute significantly to the model.

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But wait, is the model sufficient?

ask for residualsandmodificationindices, 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

What do modification indices say?

MI values greater than4 are suggestive, but thesevalues are only very approximate "hints" ofwhether modifications tomodel would lead to acceptance of additionalpathways.

All these MIs indicate that there may be a significantresidual correlation between heterogeneity and total cover. We might want to see if there is a significantresidual correlation between the two and, if so, to consider what process that would represent.

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What do residuals say?

residuals ambiguous?.

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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.

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Now we are ready to consider the results!

our unstandardized estimates

our standardized estimates

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More results

covariance betweenheterogeneity andcover is significant.

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And Still More Results

R2 for richness is pretty good, another indicator of model adequacy.