Figure 3.2 Mite damage on multiple tomato cultivars
K Bruinsma
June 17, 2018
- Information of data source
- Read in the data and view structure to identify any issues in data formatting
- Formulate hypothesis
- Conduct data exploration
- Outliers in the response variable (
Damage) within the explanatory variables (Trial,Mite,Plant.Genotype). - Collinearity of the explanatory variables
- Spatial/temporal or other hierarchical aspects of sampling design
- Interactions (is the quality of the data good enough to include them?)
- Zero inflation in Y
- Are categorical covariates balanced?
- Outliers in the response variable (
- Apply model
- Validate model
library(ggplot2) # for general plotting
library(car) # for ANOVA (Type II used, better than Type I when there is an unbalanced design)Information of data source
Damage from TU and TU-A (100 mites) on multiple tomato cultivars, 24hpi.
Read in the data and view structure to identify any issues in data formatting
damage.data <- read.csv("~/Lab Stuff/Adapted mites/Tomato/Damage assay/Adapted vs. Non-adapted on multiple cultivars/Damage R data.csv", header = TRUE)
# Trial as a factor
damage.data$Trial <- factor(damage.data$Trial)
str(damage.data)## 'data.frame': 144 obs. of 4 variables:
## $ Trial : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
## $ Mite.Strain : Factor w/ 2 levels "TU","TU-A": 1 1 1 1 1 1 1 1 1 1 ...
## $ Plant.Genotype: Factor w/ 4 levels "Castlemart","Heinz",..: 1 1 1 1 1 1 2 2 2 2 ...
## $ Damage : num 1.875 0.812 2 1.062 1 ...Formulate hypothesis
H0: There will be no difference in damage produced by the mite strains and no difference in damage between tomato cultivars.
HA: TU-A will produce more damage on all tomato cultivars compared to TU mites.
Conduct data exploration
Outliers in the response variable (Damage) within the explanatory variables (Trial, Mite, Plant.Genotype).
ggplot(damage.data, aes(x = Trial, y = Damage)) + geom_boxplot() + theme_classic()
ggplot(damage.data, aes(x = Mite.Strain, y = Damage)) + geom_boxplot() + theme_classic()
ggplot(damage.data, aes(x = Plant.Genotype, y = Damage)) + geom_boxplot() + theme_classic()
A few outliers, they seem fairly well distributed among trials and mite strains. In the interests of keeping the sample size high and balanced, I will include them unless they cause trouble during model validation.
Collinearity of the explanatory variables
Des not apply, all explanatory variables are categorical/factorial.
Spatial/temporal or other hierarchical aspects of sampling design
No, I am treating Trial as a main effect to check for reproducibility (not a random effect/blocking factor).
Interactions (is the quality of the data good enough to include them?)
Interaction betweenTrial and Mite.Strain will be performed to test for reproducibility.
Interaction betweenTrial and Plant.Genotype will be performed to test for reproducibility.
Interaction between Mite.Strain and Plant.Genotype to test if mite strains are performing the same on each tomato cultivar.
Zero inflation in Y
No
Are categorical covariates balanced?
summary(damage.data)## Trial Mite.Strain Plant.Genotype Damage
## 1:48 TU :72 Castlemart:36 Min. : 0.0625
## 2:48 TU-A:72 Heinz :36 1st Qu.: 0.7969
## 3:48 Microtom :36 Median : 4.8438
## Moneymaker:36 Mean : 21.0877
## 3rd Qu.: 34.5469
## Max. :130.3750Yes
Apply model
# fit linear model and display model fit information and ANOVA table
# full model including 3 way interaction term - to verify it is not significant, if it is, interpretation of hypothesis testing will be problematic
m.0 <- lm(Damage ~ Mite.Strain + Plant.Genotype + Trial + Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial + Mite.Strain:Plant.Genotype:Trial, data = damage.data)
summary(m.0)##
## Call:
## lm(formula = Damage ~ Mite.Strain + Plant.Genotype + Trial +
## Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial +
## Mite.Strain:Plant.Genotype:Trial, data = damage.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -63.021 -1.727 -0.089 1.089 38.229
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 1.17708 5.48150
## Mite.StrainTU-A 47.72917 7.75201
## Plant.GenotypeHeinz 0.32292 7.75201
## Plant.GenotypeMicrotom -0.78125 7.75201
## Plant.GenotypeMoneymaker 0.65625 7.75201
## Trial2 0.10417 7.75201
## Trial3 -0.26042 7.75201
## Mite.StrainTU-A:Plant.GenotypeHeinz 14.89583 10.96300
## Mite.StrainTU-A:Plant.GenotypeMicrotom -6.94792 10.96300
## Mite.StrainTU-A:Plant.GenotypeMoneymaker 42.58333 10.96300
## Mite.StrainTU-A:Trial2 -29.33333 10.96300
## Mite.StrainTU-A:Trial3 -17.51042 10.96300
## Plant.GenotypeHeinz:Trial2 -0.35417 10.96300
## Plant.GenotypeMicrotom:Trial2 -0.09375 10.96300
## Plant.GenotypeMoneymaker:Trial2 -1.11458 10.96300
## Plant.GenotypeHeinz:Trial3 0.72917 10.96300
## Plant.GenotypeMicrotom:Trial3 0.13542 10.96300
## Plant.GenotypeMoneymaker:Trial3 -0.62500 10.96300
## Mite.StrainTU-A:Plant.GenotypeHeinz:Trial2 -16.61458 15.50403
## Mite.StrainTU-A:Plant.GenotypeMicrotom:Trial2 16.70833 15.50403
## Mite.StrainTU-A:Plant.GenotypeMoneymaker:Trial2 -20.83333 15.50403
## Mite.StrainTU-A:Plant.GenotypeHeinz:Trial3 -7.86458 15.50403
## Mite.StrainTU-A:Plant.GenotypeMicrotom:Trial3 -7.16667 15.50403
## Mite.StrainTU-A:Plant.GenotypeMoneymaker:Trial3 -20.63542 15.50403
## t value Pr(>|t|)
## (Intercept) 0.215 0.830337
## Mite.StrainTU-A 6.157 1.02e-08 ***
## Plant.GenotypeHeinz 0.042 0.966842
## Plant.GenotypeMicrotom -0.101 0.919893
## Plant.GenotypeMoneymaker 0.085 0.932676
## Trial2 0.013 0.989301
## Trial3 -0.034 0.973257
## Mite.StrainTU-A:Plant.GenotypeHeinz 1.359 0.176779
## Mite.StrainTU-A:Plant.GenotypeMicrotom -0.634 0.527443
## Mite.StrainTU-A:Plant.GenotypeMoneymaker 3.884 0.000169 ***
## Mite.StrainTU-A:Trial2 -2.676 0.008500 **
## Mite.StrainTU-A:Trial3 -1.597 0.112845
## Plant.GenotypeHeinz:Trial2 -0.032 0.974282
## Plant.GenotypeMicrotom:Trial2 -0.009 0.993191
## Plant.GenotypeMoneymaker:Trial2 -0.102 0.919190
## Plant.GenotypeHeinz:Trial3 0.067 0.947081
## Plant.GenotypeMicrotom:Trial3 0.012 0.990165
## Plant.GenotypeMoneymaker:Trial3 -0.057 0.954632
## Mite.StrainTU-A:Plant.GenotypeHeinz:Trial2 -1.072 0.286037
## Mite.StrainTU-A:Plant.GenotypeMicrotom:Trial2 1.078 0.283340
## Mite.StrainTU-A:Plant.GenotypeMoneymaker:Trial2 -1.344 0.181569
## Mite.StrainTU-A:Plant.GenotypeHeinz:Trial3 -0.507 0.612903
## Mite.StrainTU-A:Plant.GenotypeMicrotom:Trial3 -0.462 0.644742
## Mite.StrainTU-A:Plant.GenotypeMoneymaker:Trial3 -1.331 0.185722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.43 on 120 degrees of freedom
## Multiple R-squared: 0.8045, Adjusted R-squared: 0.767
## F-statistic: 21.47 on 23 and 120 DF, p-value: < 2.2e-16Anova(m.0)## Anova Table (Type II tests)
##
## Response: Damage
## Sum Sq Df F value Pr(>F)
## Mite.Strain 57735 1 320.2501 < 2.2e-16 ***
## Plant.Genotype 6105 3 11.2874 1.415e-06 ***
## Trial 8078 2 22.4029 5.401e-09 ***
## Mite.Strain:Plant.Genotype 5715 3 10.5676 3.224e-06 ***
## Mite.Strain:Trial 7821 2 21.6924 9.082e-09 ***
## Plant.Genotype:Trial 1857 6 1.7171 0.1227
## Mite.Strain:Plant.Genotype:Trial 1694 6 1.5657 0.1630
## Residuals 21634 120
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# linear model without non-significant 3-way interaction (want to reduce comparisons made in Tukey-Kramer post-hoc test)
m <- lm(Damage ~ Mite.Strain + Plant.Genotype + Trial + Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial, data = damage.data)
summary(m)##
## Call:
## lm(formula = Damage ~ Mite.Strain + Plant.Genotype + Trial +
## Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial,
## data = damage.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.460 -6.161 -0.086 3.998 42.790
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -1.173 4.811 -0.244
## Mite.StrainTU-A 52.430 5.555 9.439
## Plant.GenotypeHeinz 4.403 6.414 0.686
## Plant.GenotypeMicrotom -2.372 6.414 -0.370
## Plant.GenotypeMoneymaker 7.568 6.414 1.180
## Trial2 2.697 6.211 0.434
## Trial3 4.198 6.211 0.676
## Mite.StrainTU-A:Plant.GenotypeHeinz 6.736 6.414 1.050
## Mite.StrainTU-A:Plant.GenotypeMicrotom -3.767 6.414 -0.587
## Mite.StrainTU-A:Plant.GenotypeMoneymaker 28.760 6.414 4.484
## Mite.StrainTU-A:Trial2 -34.518 5.555 -6.214
## Mite.StrainTU-A:Trial3 -26.427 5.555 -4.757
## Plant.GenotypeHeinz:Trial2 -8.661 7.856 -1.103
## Plant.GenotypeMicrotom:Trial2 8.260 7.856 1.052
## Plant.GenotypeMoneymaker:Trial2 -11.531 7.856 -1.468
## Plant.GenotypeHeinz:Trial3 -3.203 7.856 -0.408
## Plant.GenotypeMicrotom:Trial3 -3.448 7.856 -0.439
## Plant.GenotypeMoneymaker:Trial3 -10.943 7.856 -1.393
## Pr(>|t|)
## (Intercept) 0.808
## Mite.StrainTU-A 2.55e-16 ***
## Plant.GenotypeHeinz 0.494
## Plant.GenotypeMicrotom 0.712
## Plant.GenotypeMoneymaker 0.240
## Trial2 0.665
## Trial3 0.500
## Mite.StrainTU-A:Plant.GenotypeHeinz 0.296
## Mite.StrainTU-A:Plant.GenotypeMicrotom 0.558
## Mite.StrainTU-A:Plant.GenotypeMoneymaker 1.63e-05 ***
## Mite.StrainTU-A:Trial2 6.94e-09 ***
## Mite.StrainTU-A:Trial3 5.28e-06 ***
## Plant.GenotypeHeinz:Trial2 0.272
## Plant.GenotypeMicrotom:Trial2 0.295
## Plant.GenotypeMoneymaker:Trial2 0.145
## Plant.GenotypeHeinz:Trial3 0.684
## Plant.GenotypeMicrotom:Trial3 0.661
## Plant.GenotypeMoneymaker:Trial3 0.166
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.61 on 126 degrees of freedom
## Multiple R-squared: 0.7892, Adjusted R-squared: 0.7607
## F-statistic: 27.74 on 17 and 126 DF, p-value: < 2.2e-16Anova(m)## Anova Table (Type II tests)
##
## Response: Damage
## Sum Sq Df F value Pr(>F)
## Mite.Strain 57735 1 311.8491 < 2.2e-16 ***
## Plant.Genotype 6105 3 10.9913 1.842e-06 ***
## Trial 8078 2 21.8153 7.321e-09 ***
## Mite.Strain:Plant.Genotype 5715 3 10.2904 4.160e-06 ***
## Mite.Strain:Trial 7821 2 21.1233 1.227e-08 ***
## Plant.Genotype:Trial 1857 6 1.6721 0.1331
## Residuals 23327 126
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Calculate effect size and display
result.anova<-Anova(m)
ss<-result.anova$"Sum Sq" ##ss = sum of squares
pes<-ss/(ss+ss[length(ss)]) ##pes = partial e squared
pes[length(pes)]<-""
result.anova$"Part E Sq"<-pes
result.anova## Anova Table (Type II tests)
##
## Response: Damage
## Sum Sq Df F value Pr(>F) Part E Sq
## Mite.Strain 57735 1 311.8491 0.000000 0.71223
## Plant.Genotype 6105 3 10.9913 0.000002 0.20742
## Trial 8078 2 21.8153 0.000000 0.25721
## Mite.Strain:Plant.Genotype 5715 3 10.2904 0.000004 0.19679
## Mite.Strain:Trial 7821 2 21.1233 0.000000 0.25110
## Plant.Genotype:Trial 1857 6 1.6721 0.133129 0.07375
## Residuals 23327 126interaction.plot(damage.data$Plant.Genotype, damage.data$Mite.Strain, damage.data$Damage, type="l", leg.bty="o", leg.bg="grey95", lwd=2, ylab="Damage", xlab="Plant Genotype", main="Mite.Strain:Plant.Genotype")
interaction.plot(damage.data$Mite.Strain, damage.data$Trial, damage.data$Damage, type="l", leg.bty="o", leg.bg="grey95", lwd=2, ylab="Damage", xlab="Mite Strain", main="Mite.Strain:Trial")
interaction.plot(damage.data$Plant.Genotype, damage.data$Trial, damage.data$Damage, type="l", leg.bty="o", leg.bg="grey95", lwd=2, ylab="Damage", xlab="Plant Genotype", main="Plant Genotype:Trial")
# perform post-hoc Tukey-Kramer test of contrasts
TukeyHSD(aov(Damage ~ Mite.Strain + Plant.Genotype + Trial + Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial, data = damage.data))## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Damage ~ Mite.Strain + Plant.Genotype + Trial + Mite.Strain:Plant.Genotype + Mite.Strain:Trial + Plant.Genotype:Trial, data = damage.data)
##
## $Mite.Strain
## diff lwr upr p adj
## TU-A-TU 40.04687 35.55905 44.5347 0
##
## $Plant.Genotype
## diff lwr upr p adj
## Heinz-Castlemart 3.815972 -4.534168 12.166112 0.6343748
## Microtom-Castlemart -2.651042 -11.001182 5.699098 0.8417565
## Moneymaker-Castlemart 14.456597 6.106457 22.806737 0.0000865
## Microtom-Heinz -6.467014 -14.817154 1.883126 0.1874106
## Moneymaker-Heinz 10.640625 2.290485 18.990765 0.0064368
## Moneymaker-Microtom 17.107639 8.757499 25.457779 0.0000026
##
## $Trial
## diff lwr upr p adj
## 2-1 -17.54557 -24.132875 -10.95827 0.0000000
## 3-1 -13.41406 -20.001365 -6.82676 0.0000116
## 3-2 4.13151 -2.455792 10.71881 0.3003297
##
## $`Mite.Strain:Plant.Genotype`
## diff lwr upr
## TU-A:Castlemart-TU:Castlemart 32.11458333 18.133812 46.095354
## TU:Heinz-TU:Castlemart 0.44791667 -13.532854 14.428688
## TU-A:Heinz-TU:Castlemart 39.29861111 25.317840 53.279382
## TU:Microtom-TU:Castlemart -0.76736111 -14.748132 13.213410
## TU-A:Microtom-TU:Castlemart 27.57986111 13.599090 41.560632
## TU:Moneymaker-TU:Castlemart 0.07638889 -13.904382 14.057160
## TU-A:Moneymaker-TU:Castlemart 60.95138889 46.970618 74.932160
## TU:Heinz-TU-A:Castlemart -31.66666667 -45.647438 -17.685896
## TU-A:Heinz-TU-A:Castlemart 7.18402778 -6.796743 21.164799
## TU:Microtom-TU-A:Castlemart -32.88194444 -46.862716 -18.901173
## TU-A:Microtom-TU-A:Castlemart -4.53472222 -18.515493 9.446049
## TU:Moneymaker-TU-A:Castlemart -32.03819444 -46.018966 -18.057423
## TU-A:Moneymaker-TU-A:Castlemart 28.83680556 14.856034 42.817577
## TU-A:Heinz-TU:Heinz 38.85069444 24.869923 52.831466
## TU:Microtom-TU:Heinz -1.21527778 -15.196049 12.765493
## TU-A:Microtom-TU:Heinz 27.13194444 13.151173 41.112716
## TU:Moneymaker-TU:Heinz -0.37152778 -14.352299 13.609243
## TU-A:Moneymaker-TU:Heinz 60.50347222 46.522701 74.484243
## TU:Microtom-TU-A:Heinz -40.06597222 -54.046743 -26.085201
## TU-A:Microtom-TU-A:Heinz -11.71875000 -25.699521 2.262021
## TU:Moneymaker-TU-A:Heinz -39.22222222 -53.202993 -25.241451
## TU-A:Moneymaker-TU-A:Heinz 21.65277778 7.672007 35.633549
## TU-A:Microtom-TU:Microtom 28.34722222 14.366451 42.327993
## TU:Moneymaker-TU:Microtom 0.84375000 -13.137021 14.824521
## TU-A:Moneymaker-TU:Microtom 61.71875000 47.737979 75.699521
## TU:Moneymaker-TU-A:Microtom -27.50347222 -41.484243 -13.522701
## TU-A:Moneymaker-TU-A:Microtom 33.37152778 19.390757 47.352299
## TU-A:Moneymaker-TU:Moneymaker 60.87500000 46.894229 74.855771
## p adj
## TU-A:Castlemart-TU:Castlemart 0.0000000
## TU:Heinz-TU:Castlemart 1.0000000
## TU-A:Heinz-TU:Castlemart 0.0000000
## TU:Microtom-TU:Castlemart 0.9999998
## TU-A:Microtom-TU:Castlemart 0.0000004
## TU:Moneymaker-TU:Castlemart 1.0000000
## TU-A:Moneymaker-TU:Castlemart 0.0000000
## TU:Heinz-TU-A:Castlemart 0.0000000
## TU-A:Heinz-TU-A:Castlemart 0.7589948
## TU:Microtom-TU-A:Castlemart 0.0000000
## TU-A:Microtom-TU-A:Castlemart 0.9737029
## TU:Moneymaker-TU-A:Castlemart 0.0000000
## TU-A:Moneymaker-TU-A:Castlemart 0.0000001
## TU-A:Heinz-TU:Heinz 0.0000000
## TU:Microtom-TU:Heinz 0.9999948
## TU-A:Microtom-TU:Heinz 0.0000006
## TU:Moneymaker-TU:Heinz 1.0000000
## TU-A:Moneymaker-TU:Heinz 0.0000000
## TU:Microtom-TU-A:Heinz 0.0000000
## TU-A:Microtom-TU-A:Heinz 0.1717221
## TU:Moneymaker-TU-A:Heinz 0.0000000
## TU-A:Moneymaker-TU-A:Heinz 0.0001308
## TU-A:Microtom-TU:Microtom 0.0000002
## TU:Moneymaker-TU:Microtom 0.9999996
## TU-A:Moneymaker-TU:Microtom 0.0000000
## TU:Moneymaker-TU-A:Microtom 0.0000004
## TU-A:Moneymaker-TU-A:Microtom 0.0000000
## TU-A:Moneymaker-TU:Moneymaker 0.0000000
##
## $`Mite.Strain:Trial`
## diff lwr upr p adj
## TU-A:1-TU:1 60.3619792 48.994489 71.72947 0.0000000
## TU:2-TU:1 -0.2864583 -11.653948 11.08103 0.9999997
## TU-A:2-TU:1 25.5572917 14.189802 36.92478 0.0000000
## TU:3-TU:1 -0.2005208 -11.568011 11.16697 1.0000000
## TU-A:3-TU:1 33.7343750 22.366885 45.10186 0.0000000
## TU:2-TU-A:1 -60.6484375 -72.015927 -49.28095 0.0000000
## TU-A:2-TU-A:1 -34.8046875 -46.172177 -23.43720 0.0000000
## TU:3-TU-A:1 -60.5625000 -71.929990 -49.19501 0.0000000
## TU-A:3-TU-A:1 -26.6276042 -37.995094 -15.26011 0.0000000
## TU-A:2-TU:2 25.8437500 14.476260 37.21124 0.0000000
## TU:3-TU:2 0.0859375 -11.281552 11.45343 1.0000000
## TU-A:3-TU:2 34.0208333 22.653344 45.38832 0.0000000
## TU:3-TU-A:2 -25.7578125 -37.125302 -14.39032 0.0000000
## TU-A:3-TU-A:2 8.1770833 -3.190406 19.54457 0.3034916
## TU-A:3-TU:3 33.9348958 22.567406 45.30239 0.0000000
##
## $`Plant.Genotype:Trial`
## diff lwr upr p adj
## Heinz:1-Castlemart:1 7.7708333 -10.7292326 26.2708992 0.9617476
## Microtom:1-Castlemart:1 -4.2552083 -22.7552742 14.2448576 0.9997880
## Moneymaker:1-Castlemart:1 21.9479167 3.4478508 40.4479826 0.0069065
## Castlemart:2-Castlemart:1 -14.5625000 -33.0625659 3.9375659 0.2792220
## Heinz:2-Castlemart:1 -15.4531250 -33.9531909 3.0469409 0.2006691
## Microtom:2-Castlemart:1 -10.5572917 -29.0573576 7.9427742 0.7566532
## Moneymaker:2-Castlemart:1 -4.1458333 -22.6458992 14.3542326 0.9998355
## Castlemart:3-Castlemart:1 -9.0156250 -27.5156909 9.4844409 0.8973777
## Heinz:3-Castlemart:1 -4.4479167 -22.9479826 14.0521492 0.9996751
## Microtom:3-Castlemart:1 -16.7187500 -35.2188159 1.7813159 0.1180125
## Moneymaker:3-Castlemart:1 1.9895833 -16.5104826 20.4896492 0.9999999
## Microtom:1-Heinz:1 -12.0260417 -30.5261076 6.4740242 0.5777402
## Moneymaker:1-Heinz:1 14.1770833 -4.3229826 32.6771492 0.3183949
## Castlemart:2-Heinz:1 -22.3333333 -40.8333992 -3.8332674 0.0054113
## Heinz:2-Heinz:1 -23.2239583 -41.7240242 -4.7238924 0.0030316
## Microtom:2-Heinz:1 -18.3281250 -36.8281909 0.1719409 0.0546102
## Moneymaker:2-Heinz:1 -11.9166667 -30.4167326 6.5833992 0.5917282
## Castlemart:3-Heinz:1 -16.7864583 -35.2865242 1.7136076 0.1144866
## Heinz:3-Heinz:1 -12.2187500 -30.7188159 6.2813159 0.5530555
## Microtom:3-Heinz:1 -24.4895833 -42.9896492 -5.9895174 0.0012844
## Moneymaker:3-Heinz:1 -5.7812500 -24.2813159 12.7188159 0.9963931
## Moneymaker:1-Microtom:1 26.2031250 7.7030591 44.7031909 0.0003778
## Castlemart:2-Microtom:1 -10.3072917 -28.8073576 8.1927742 0.7836774
## Heinz:2-Microtom:1 -11.1979167 -29.6979826 7.3021492 0.6818518
## Microtom:2-Microtom:1 -6.3020833 -24.8021492 12.1979826 0.9924800
## Moneymaker:2-Microtom:1 0.1093750 -18.3906909 18.6094409 1.0000000
## Castlemart:3-Microtom:1 -4.7604167 -23.2604826 13.7396492 0.9993808
## Heinz:3-Microtom:1 -0.1927083 -18.6927742 18.3073576 1.0000000
## Microtom:3-Microtom:1 -12.4635417 -30.9636076 6.0365242 0.5217575
## Moneymaker:3-Microtom:1 6.2447917 -12.2552742 24.7448576 0.9930316
## Castlemart:2-Moneymaker:1 -36.5104167 -55.0104826 -18.0103508 0.0000001
## Heinz:2-Moneymaker:1 -37.4010417 -55.9011076 -18.9009758 0.0000000
## Microtom:2-Moneymaker:1 -32.5052083 -51.0052742 -14.0051424 0.0000025
## Moneymaker:2-Moneymaker:1 -26.0937500 -44.5938159 -7.5936841 0.0004093
## Castlemart:3-Moneymaker:1 -30.9635417 -49.4636076 -12.4634758 0.0000092
## Heinz:3-Moneymaker:1 -26.3958333 -44.8958992 -7.8957674 0.0003279
## Microtom:3-Moneymaker:1 -38.6666667 -57.1667326 -20.1666008 0.0000000
## Moneymaker:3-Moneymaker:1 -19.9583333 -38.4583992 -1.4582674 0.0226894
## Heinz:2-Castlemart:2 -0.8906250 -19.3906909 17.6094409 1.0000000
## Microtom:2-Castlemart:2 4.0052083 -14.4948576 22.5052742 0.9998827
## Moneymaker:2-Castlemart:2 10.4166667 -8.0833992 28.9167326 0.7720264
## Castlemart:3-Castlemart:2 5.5468750 -12.9531909 24.0469409 0.9974930
## Heinz:3-Castlemart:2 10.1145833 -8.3854826 28.6146492 0.8035122
## Microtom:3-Castlemart:2 -2.1562500 -20.6563159 16.3438159 0.9999998
## Moneymaker:3-Castlemart:2 16.5520833 -1.9479826 35.0521492 0.1270576
## Microtom:2-Heinz:2 4.8958333 -13.6042326 23.3958992 0.9991951
## Moneymaker:2-Heinz:2 11.3072917 -7.1927742 29.8073576 0.6684490
## Castlemart:3-Heinz:2 6.4375000 -12.0625659 24.9375659 0.9910346
## Heinz:3-Heinz:2 11.0052083 -7.4948576 29.5052742 0.7050736
## Microtom:3-Heinz:2 -1.2656250 -19.7656909 17.2344409 1.0000000
## Moneymaker:3-Heinz:2 17.4427083 -1.0573576 35.9427742 0.0845013
## Moneymaker:2-Microtom:2 6.4114583 -12.0886076 24.9115242 0.9913286
## Castlemart:3-Microtom:2 1.5416667 -16.9583992 20.0417326 1.0000000
## Heinz:3-Microtom:2 6.1093750 -12.3906909 24.6094409 0.9942055
## Microtom:3-Microtom:2 -6.1614583 -24.6615242 12.3386076 0.9937748
## Moneymaker:3-Microtom:2 12.5468750 -5.9531909 31.0469409 0.5111487
## Castlemart:3-Moneymaker:2 -4.8697917 -23.3698576 13.6302742 0.9992341
## Heinz:3-Moneymaker:2 -0.3020833 -18.8021492 18.1979826 1.0000000
## Microtom:3-Moneymaker:2 -12.5729167 -31.0729826 5.9271492 0.5078403
## Moneymaker:3-Moneymaker:2 6.1354167 -12.3646492 24.6354826 0.9939933
## Heinz:3-Castlemart:3 4.5677083 -13.9323576 23.0677742 0.9995811
## Microtom:3-Castlemart:3 -7.7031250 -26.2031909 10.7969409 0.9640767
## Moneymaker:3-Castlemart:3 11.0052083 -7.4948576 29.5052742 0.7050736
## Microtom:3-Heinz:3 -12.2708333 -30.7708992 6.2292326 0.5463855
## Moneymaker:3-Heinz:3 6.4375000 -12.0625659 24.9375659 0.9910346
## Moneymaker:3-Microtom:3 18.7083333 0.2082674 37.2083992 0.0448690The interaction between Mite.Strain and Trial seems to be due to the fact that there is a lot of variability in the damage done by TU-A mites in the different trials, but the TU mites produced generally the same amount of damage (near zero).
Validate model
damage.data$m.fit <- fitted(m) # fitted values
damage.data$m.res <- rstandard(m) # Pearson residualsResidual distribution / Overdispersion
We assumed normal residuals. This is the least important regression assumption but its ca be tested with a qq plot.
ggplot(damage.data, aes(sample = m.res)) + geom_qq() + geom_abline(intercept = 0, slope = 1) + theme_classic() 
Decent.
Residuals vs fitted values
Testing for:
Linearity - there should be no curvilinear pattern in the residuals.
Equal variance - the vertical spread of the residuals should be constant across all fitted values.
ggplot(damage.data, aes(x = m.fit, y = m.res)) +
geom_point() + geom_hline(yintercept = 0) + geom_smooth() + theme_classic()## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Linearity - pretty good - confidence interval includes 0. Fairly even spread of residuals
Residuals vs explanatory variables
Should be centered around 0, if not then model requires another explanatory variable(s), to account for observed variation.
ggplot(damage.data, aes(x = Mite.Strain, y = m.res)) +
geom_boxplot() + geom_hline(yintercept = 0) + theme_classic()
ggplot(damage.data, aes(x = Trial, y = m.res)) +
geom_boxplot() + geom_hline(yintercept = 0) + theme_classic()
ggplot(damage.data, aes(x = Plant.Genotype, y = m.res)) +
geom_boxplot() + geom_hline(yintercept = 0) + theme_classic()