Diamondback Moth Egg Counts on Braya species

1
Diamondback Moth Egg Counts on Braya species

• Susan Tilley
• Biology 7932

2
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 B0 BSXS BYXY BDXD BTXT BSYXSY
  BSDXSD BSTXST BYDXYD BYTXYT
  BDTXDT BSYDXSYD BSYTXSYT
  BSDTXSDT BYDTXYDT BSYDTXSYDT
  error

3
Evaluation of Model Using Residuals

4
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
• SY 2 28.577 25.269 12.635
  5.15 0.006
• SD 1 46.306 33.451 33.451
  13.63 0.000
• ST 3 136.640 86.249 28.750
  11.71 0.000
• YD 2 3.621 3.150 1.575
  0.64 0.527
• YT 6 126.922 88.758 14.793
  6.03 0.000
• DT 3 85.836 52.000 17.333
  7.06 0.000
• SYD 2 31.148 19.914 9.957
  4.06 0.017
• SYT 6 30.202 25.190 4.198
  1.71 0.115
• SDT [phone]
  3.44 0.016
• YDT 6 8.220 6.533 1.089
  0.44 0.850
• SYDT 6 17.977 17.977 2.996
  1.22 0.292
• Error 2643 6488.822 6488.822 2.455
• Total 2690 8295.825

5
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

6
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

1 Presence 2 Absence
7
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
8
LR Statistics For Type 1 Analysis

• Chi-
• Source Deviance DF Square Pr
  gt ChiSq
• Intercept 3003.2023
• S 2930.6693 1 72.53
  lt.0001
• Y 2859.5837 2 71.09
  lt.0001
• D 2817.4975 1 42.09
  lt.0001
• T 2492.4354 3 325.06
  lt.0001
• SY 2484.5770 2 7.86
  0.0197
• SD 2473.0021 1 11.57
  0.0007
• ST 2471.0216 3 1.98
  0.5765
• YD 2462.6702 2 8.35
  0.0154
• YT 2457.9981 6 4.67
  0.5865
• DT 2453.7222 3 4.28
  0.2332
• SYD 2448.1246 2 5.60
  0.0609
• SYT 2443.2222 6 4.90
  0.5564
• SDT [phone]
  0.4099
• YDT 2435.4702 6 4.87
  0.5608
• SYDT 2422.0342 6 13.44
  0.0366

9
Generalized Linear Model Binomial
DistributionBraya 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
10
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
11
LR Statistics For Type 1 Analysis
Braya longii
Chi- Source Deviance DF
Square Pr gt ChiSq Intercept 1933.6586 Y
1882.6239 2 51.03
lt.0001 D 1842.9210 1
39.70 lt.0001 T 1600.3273
3 242.59 lt.0001 YD
1598.7296 2 1.60 0.4499 YT
1592.3175 6 6.41
0.3786 DT 1587.1275 3
5.19 0.1584 YDT 1578.9682
6 8.16 0.2267
12
LR Statistics For Type 1 Analysis
Braya fernaldii

Chi- Source Deviance DF Square
Pr gt ChiSq Intercept 997.0107 Y
968.0396 2 28.97 lt.0001 D
963.7795 1 4.26
0.0390 T 870.6944 3
93.09 lt.0001 YD 859.8225
2 10.87 0.0044 YT
856.2523 6 3.57 0.7346 DT
853.2107 3 3.04
0.3853 YDT 843.0660 6
10.14 0.1187
13
BL Braya longii BF Braya fernaldii N
Natural Disturbance D Anthropogenic Disturbance
14
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

15
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
16
LR Statistics For Type 1 Analysis

• Chi-
• Source Deviance DF Square
  Pr gt ChiSq
• Intercept 6139.6847
• S 5786.3804 1 353.30
  lt.0001
• Y 5483.9630 2 302.42
  lt.0001
• D 5358.0698 1 125.89
  lt.0001
• T 4157.7239 3 1200.35
  lt.0001
• SY 4126.7328 2 30.99
  lt.0001
• SD 4103.3052 1 23.43
  lt.0001
• ST 4099.5266 3 3.78
  0.2864
• YD 4091.1411 2 8.39
  0.0151
• YT 4069.7446 6 21.40
  0.0016
• DT 4059.2600 3 10.48
  0.0149
• SYD 4035.4374 2 23.82
  lt.0001
• SYT 4028.7876 6 6.65
  0.3544
• SDT [phone]
  0.0972
• YDT 4009.7178 6 12.75
  0.0471
• SYDT 3989.7034 6 20.01
  0.0028

17
Pearson Chi-Square 0.98 2.37 1.08 1.93 1.14
Binomial Poisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only
S 72.53 353.3 90.91 48.6 27.36
Y 71.09 302.42 81.57 35.73 20.48
D 42.09 125.89 35.14 7.65 3.99
T 325.06 1200.35 376.31 135.09 80.1
SY 7.86 30.99 13.06 3.00 2.09
SD 11.57 23.43 5.15 2.09 1.04
ST 1.98 3.78 0.99 3.08 2.29
YD 8.35 8.39 3.51 2.44 1.88
YT 4.67 21.4 8.28 5.09 3.32
DT 4.28 10.48 6.08 3.16 2.09
SYD 5.6 23.82 9.64 7.67 4.79
SYT 4.9 6.65 5.32 3.61 2.76
SDT 2.88 6.32 4.45 0.71 0.51
YDT 4.87 12.75 8.72 10.2 6.86
SYDT 13.44 20.01 16.52 2.91 2.18
18
Pearson Chi-Square 0.98 2.37 1.08 1.93 1.14
Binomial Poisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only
S 72.53 353.3 90.91 48.6 27.36
Y 71.09 302.42 81.57 35.73 20.48
D 42.09 125.89 35.14 7.65 3.99
T 325.06 1200.35 376.31 135.09 80.1
SY 7.86 30.99 13.06 3.00 2.09
SD 11.57 23.43 5.15 2.09 1.04
ST 1.98 3.78 0.99 3.08 2.29
YD 8.35 8.39 3.51 2.44 1.88
YT 4.67 21.4 8.28 5.09 3.32
DT 4.28 10.48 6.08 3.16 2.09
SYD 5.6 23.82 9.64 7.67 4.79
SYT 4.9 6.65 5.32 3.61 2.76
SDT 2.88 6.32 4.45 0.71 0.51
YDT 4.87 12.75 8.72 10.2 6.86
SYDT 13.44 20.01 16.52 2.91 2.18
19
Pearson Chi-Square 0.98 2.37 1.08 1.93 1.14
Binomial Poisson Negative Binomial Poisson Eggs Only Negative Binomial Eggs Only
S 72.53 353.3 90.91 48.6 27.36
Y 71.09 302.42 81.57 35.73 20.48
D 42.09 125.89 35.14 7.65 3.99
T 325.06 1200.35 376.31 135.09 80.1
SY 7.86 30.99 13.06 3.00 2.09
SD 11.57 23.43 5.15 2.09 1.04
ST 1.98 3.78 0.99 3.08 2.29
YD 8.35 8.39 3.51 2.44 1.88
YT 4.67 21.4 8.28 5.09 3.32
DT 4.28 10.48 6.08 3.16 2.09
SYD 5.6 23.82 9.64 7.67 4.79
SYT 4.9 6.65 5.32 3.61 2.76
SDT 2.88 6.32 4.45 0.71 0.51
YDT 4.87 12.75 8.72 10.2 6.86
SYDT 13.44 20.01 16.52 2.91 2.18
20
Conclusions

• Binomial model is better than Poisson model
  because Pearson Chi-Square is closer to 1.
• The questions of
• why is an organism present or absent?
• 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

21

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

22
The very longAnalysis of Parameter
EstimatesTable