# Diamondback Moth Egg Counts on Braya species Susan Tilley Biology 7932.

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Diamondback Moth Egg Counts on Braya species Susan Tilley Biology 7932

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

Evaluation of Model Using Residuals

ANOVA Source DF Seq SS Adj SS Adj MS F P S 1 211.259 114.405 114.405 46.60 0.000 Y 2 188.106 91.729 45.865 18.68 0.000 D 1 89.351 39.490 39.490 16.08 0.000 T 3 777.429 518.975 172.992 70.46 0.000 S*Y 2 28.577 25.269 12.635 5.15 0.006 S*D 1 46.306 33.451 33.451 13.63 0.000 S*T 3 136.640 86.249 28.750 11.71 0.000 Y*D 2 3.621 3.150 1.575 0.64 0.527 Y*T 6 126.922 88.758 14.793 6.03 0.000 D*T 3 85.836 52.000 17.333 7.06 0.000 S*Y*D 2 31.148 19.914 9.957 4.06 0.017 S*Y*T 6 30.202 25.190 4.198 1.71 0.115 S*D*T 3 25.409 25.350 8.450 3.44 0.016 Y*D*T 6 8.220 6.533 1.089 0.44 0.850 S*Y*D*T 6 17.977 17.977 2.996 1.22 0.292 Error 2643 6488.822 6488.822 2.455 Total 2690 8295.825

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

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 2 1 2 Y 3 1 2 3 D 2 1 2 T 4 1 2 3 4 Response Profile Ordered Total Value PE Frequency 1 1 662 2 2 2030 1 = Presence 2 = Absence

Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 2644 2422.0342 0.9160 Scaled Deviance 2644 2422.0342 0.9160 Pearson Chi-Square 2644 2601.0000 0.9837 Scaled Pearson X2 2644 2601.0000 0.983 Log Likelihood -1211.0171

LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept 3003.2023 S 2930.6693 1 72.53 <.0001 Y 2859.5837 2 71.09 <.0001 D 2817.4975 1 42.09 <.0001 T 2492.4354 3 325.06 <.0001 S*Y 2484.5770 2 7.86 0.0197 S*D 2473.0021 1 11.57 0.0007 S*T 2471.0216 3 1.98 0.5765 Y*D 2462.6702 2 8.35 0.0154 Y*T 2457.9981 6 4.67 0.5865 D*T 2453.7222 3 4.28 0.2332 S*Y*D 2448.1246 2 5.60 0.0609 S*Y*T 2443.2222 6 4.90 0.5564 S*D*T 2440.3382 3 2.88 0.4099 Y*D*T 2435.4702 6 4.87 0.5608 S*Y*D*T 2422.0342 6 13.44 0.0366

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

Criteria For Assessing Goodness Of Fit Braya longii Criterion DF Value Value/DF Deviance 1549 1578.9682 1.0193 Scaled Deviance 1549 1578.9682 1.0193 Pearson Chi-Square 1549 1523.0000 0.9832 Scaled Pearson X2 1549 1523.0000 0.9832 Log Likelihood -789.4841 Braya fernaldii Criterion DF Value Value/DF Deviance 1095 843.0660 0.7699 Scaled Deviance 1095 843.0660 0.7699 Pearson Chi-Square 1095 1078.0000 0.9845 Scaled Pearson X2 1095 1078.0000 0.9845 Log Likelihood -421.5330

LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept 1933.6586 Y 1882.6239 2 51.03 <.0001 D 1842.9210 1 39.70 <.0001 T 1600.3273 3 242.59 <.0001 Y*D 1598.7296 2 1.60 0.4499 Y*T 1592.3175 6 6.41 0.3786 D*T 1587.1275 3 5.19 0.1584 Y*D*T 1578.9682 6 8.16 0.2267 Braya longii

LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept 997.0107 Y 968.0396 2 28.97 <.0001 D 963.7795 1 4.26 0.0390 T 870.6944 3 93.09 <.0001 Y*D 859.8225 2 10.87 0.0044 Y*T 856.2523 6 3.57 0.7346 D*T 853.2107 3 3.04 0.3853 Y*D*T 843.0660 6 10.14 0.1187 Braya fernaldii

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

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 2 1 2 Y 3 1 2 3 D 2 1 2 T 4 1 2 3 4

Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 2644 3989.7034 1.5090 Scaled Deviance 2644 3989.7034 1.5090 Pearson Chi-Square 2644 6275.5418 2.3735 Scaled Pearson X2 2644 6275.5418 2.3735 Log Likelihood -1431.6801

LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept 6139.6847 S 5786.3804 1 353.30 <.0001 Y 5483.9630 2 302.42 <.0001 D 5358.0698 1 125.89 <.0001 T 4157.7239 3 1200.35 <.0001 S*Y 4126.7328 2 30.99 <.0001 S*D 4103.3052 1 23.43 <.0001 S*T 4099.5266 3 3.78 0.2864 Y*D 4091.1411 2 8.39 0.0151 Y*T 4069.7446 6 21.40 0.0016 D*T 4059.2600 3 10.48 0.0149 S*Y*D 4035.4374 2 23.82 <.0001 S*Y*T 4028.7876 6 6.65 0.3544 S*D*T 4022.4713 3 6.32 0.0972 Y*D*T 4009.7178 6 12.75 0.0471 S*Y*D*T 3989.7034 6 20.01 0.0028

Pearson Chi-Square 0.982.371.081.931.14 BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S72.53353.390.9148.627.36 Y71.09302.4281.5735.7320.48 D42.09125.8935.147.653.99 T325.061200.35376.31135.0980.1 S*Y7.8630.9913.063.002.09 S*D11.5723.435.152.091.04 S*T1.983.780.993.082.29 Y*D8.358.393.512.441.88 Y*T4.6721.48.285.093.32 D*T4.2810.486.083.162.09 S*Y*D5.623.829.647.674.79 S*Y*T4.96.655.323.612.76 S*D*T2.886.324.450.710.51 Y*D*T4.8712.758.7210.26.86 S*Y*D*T13.4420.0116.522.912.18

Pearson Chi-Square 0.982.371.081.931.14 BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S72.53353.390.9148.627.36 Y71.09302.4281.5735.7320.48 D42.09125.8935.147.653.99 T325.061200.35376.31135.0980.1 S*Y7.8630.9913.063.002.09 S*D11.5723.435.152.091.04 S*T1.983.780.993.082.29 Y*D8.358.393.512.441.88 Y*T4.6721.48.285.093.32 D*T4.2810.486.083.162.09 S*Y*D5.623.829.647.674.79 S*Y*T4.96.655.323.612.76 S*D*T2.886.324.450.710.51 Y*D*T4.8712.758.7210.26.86 S*Y*D*T13.4420.0116.522.912.18

Pearson Chi-Square 0.982.371.081.931.14 BinomialPoisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only S72.53353.390.9148.627.36 Y71.09302.4281.5735.7320.48 D42.09125.8935.147.653.99 T325.061200.35376.31135.0980.1 S*Y7.8630.9913.063.002.09 S*D11.5723.435.152.091.04 S*T1.983.780.993.082.29 Y*D8.358.393.512.441.88 Y*T4.6721.48.285.093.32 D*T4.2810.486.083.162.09 S*Y*D5.623.829.647.674.79 S*Y*T4.96.655.323.612.76 S*D*T2.886.324.450.710.51 Y*D*T4.8712.758.7210.26.86 S*Y*D*T13.4420.0116.522.912.18

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

Littell, et al. (2002) SAS for Linear Models http://faculty.ucr.edu/~hanneman/linear_models/index.html Contains SAS files used in textbook

The very longAnalysis of Parameter Estimates Table

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