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Diamondback Moth Egg Counts on Braya species Susan Tilley Biology 7932

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Can egg numbers be explained by species, year, disturbance or plant type? Response Variable: Number of Eggs (E) Explanatory Variable: Species (S) – 2 Year (Y) - 3 Disturbance (D) - 2 Plant Type (T) - 4 E= B 0 + B S X S + B Y X Y + B D X D + B T X T + B S*Y X S*Y + B S*D X S*D + B S*T X S*T + B Y*D X Y*D + B Y*T X Y*T + B D*T X D*T + B S*Y*D X S*Y*D + B S*Y*T X S*Y*T + B S*D*T X S*D*T + B Y*D*T X Y*D*T + B S*Y*D*T X S*Y*D*T + error

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Evaluation of Model Using Residuals

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ANOVA Source DF Seq SS Adj SS Adj MS F P S Y D T S*Y S*D S*T Y*D Y*T D*T S*Y*D S*Y*T S*D*T Y*D*T S*Y*D*T Error Total

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Poisson or Binomial? Lots of zeros in count data therefore Poisson is next step BUT… 1 egg = damage THEREFORE Can use presence/absence of eggs in analysis

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Generalized Linear Model: Binomial Distribution Model Information Data Set WORK.COUNTS Distribution Binomial Link Function Logit Dependent Variable PE Number of Observations Read 2692 Number of Observations Used 2692 Number of Events 662 Number of Trials 2692 Class Level Information Class Levels Values S Y D T Response Profile Ordered Total Value PE Frequency = Presence 2 = Absence

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Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood

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LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept S <.0001 Y <.0001 D <.0001 T <.0001 S*Y S*D S*T Y*D Y*T D*T S*Y*D S*Y*T S*D*T Y*D*T S*Y*D*T

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Generalized Linear Model: Binomial Distribution Braya longii Braya fernaldii Model Information Distribution Binomial Link Function Logit Dependent Variable PE Number of Observations Read 1573 Number of Observations Used 1573 Number of Events 479 Number of Trials 1573 Model Information Distribution Binomial Link Function Logit Dependent Variable PE Number of Observations Read 1119 Number of Observations Used 1119 Number of Events 183 Number of Trials 1119

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Criteria For Assessing Goodness Of Fit Braya longii Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood Braya fernaldii Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood

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LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept Y <.0001 D <.0001 T <.0001 Y*D Y*T D*T Y*D*T Braya longii

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LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept Y <.0001 D T <.0001 Y*D Y*T D*T Y*D*T Braya fernaldii

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BL= Braya longii BF= Braya fernaldii N= Natural Disturbance D= Anthropogenic Disturbance

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Generalized Linear Model: Poisson Distribution Model Information Data Set WORK.COUNTS Distribution Poisson Link Function Log Dependent Variable E Number of Observations Read 2692 Number of Observations Used 2692 Class Level Information Class Levels Values S Y D T

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Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood

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LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept S <.0001 Y <.0001 D <.0001 T <.0001 S*Y <.0001 S*D <.0001 S*T Y*D Y*T D*T S*Y*D <.0001 S*Y*T S*D*T Y*D*T S*Y*D*T

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Pearson Chi-Square BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S Y D T S*Y S*D S*T Y*D Y*T D*T S*Y*D S*Y*T S*D*T Y*D*T S*Y*D*T

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Pearson Chi-Square BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S Y D T S*Y S*D S*T Y*D Y*T D*T S*Y*D S*Y*T S*D*T Y*D*T S*Y*D*T

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Pearson Chi-Square BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S Y D T S*Y S*D S*T Y*D Y*T D*T S*Y*D S*Y*T S*D*T Y*D*T S*Y*D*T

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Conclusions Binomial model is better than Poisson model because Pearson Chi-Square is closer to 1. The questions of: 1. 1.why is an organism present or absent? 2. 2.what controls the abundance of an organism that is present? are very different and therefore should be analyzed separately. Presence/Absence = Binomial What controls abundance once present = Poisson, Negative Binomial, and Poisson with scale factor

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Littell, et al. (2002) SAS for Linear Models Contains SAS files used in textbook

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The very longAnalysis of Parameter Estimates Table

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