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

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2 A Graphical View of the Univariate Model

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

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4 Pruned Univariate Model

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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!

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6 Our Structural Equation Model

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

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

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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).

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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.

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11 What do residuals say? residuals ambiguous?.

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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.

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

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14 More results covariance between heterogeneity and cover is significant.

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

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