1. A preliminary exploration into the Binomial Logistic Regression Models in R and their potential application Andrew Trant PPS Arctic - Labrador Highlands Research Group

2. One presentation in two parts Part 1 (today) -comparing binomial logistical regressions in R and Minitab -binomial GLMs and Odds Ratios Part 2 (next time) -using GLMs in conservation biology -an exploration of the past

3. Start off small….. before …and after Kettlewell, H B D (1956)

4. Research Question: Are the odds of survival higher for dark form (Melanic) than the light form (Typical)? Odds = e (  o) + e (  Type) + error (link = logit)

5. In Minitab: In R…

6. glm(formula = Nrecap/Nrel ~ type, family = binomial, data = moth,weights = Nrel) Call: Coefficients: (Intercept) typeTyp -0.6584 -0.9332 Degrees of Freedom: 1 Total (i.e. Null); 0 Residual Null Deviance: 22.98 Residual Deviance: 1.592e-13 AIC: 15.93 > summary(moth) Deviance Residuals: [1] 0 0 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.65840 0.08604 -7.652 1.98e-14 *** typeTyp -0.93323 0.20689 -4.511 6.46e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 2.2977e+01 on 1 degrees of freedom Residual deviance: 1.5921e-13 on 0 degrees of freedom AIC: 15.929 Number of Fisher Scoring iterations: 3

7. In Minitab: In R… Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

8. Odds = e (  o) + e (  Type) + error BUT R assumes that  o = melanistic NOT typical > exp(-0.6584) = 0.5176 R: MINITAB: >exp(-1.5916+0.9332) = 0.5177

9. Odds = e (  o) + e (  Type) + error BUT R assumes that  o = melanistic NOT typical > exp(-0.6584) = 0.5176 R: MINITAB: >exp(-1.5916+0.9332) = 0.5177 SAME(ish)

10. R: MINITAB: >exp(0.9332) = 2.5426 Odds Ratio >exp(-0.9332) = 0.3933 >1/exp(-0.9332)=2.5426

11. Calculating 95% Confidence Intervals CI = e Estimate±(SE*z-value) >exp(0.9332±(0.2069*1.96)) Lower = 1.694989 Upper= 3.814174

12. You have reached the end of part one But there is a preliminary stab at part two

13. Dave’s Barnacles Tetraclita squamosa Acanthia sp. >avthickathole<-glm(formula=Npartial/N~AvThickAtHole,family=binomial, weights=N,data=test)

14. Average thickness at hole LM GLM

15. Average thickness at hole General Linear Model: >lm.avthickathole<-lm(w.wbar~AvThickAtHole,data=test) Generalized Linear Model: >avthickathole<-glm(formula=Npartial/N~AvThickAtHole,family=binomial, weights=N,data=test) Odds Ratio: 1.13 (remember…exp(0.1249))

16. Average thickness residuals plots LM GLM

17. Summary of model comparison…GLM vs LM

18. Height of barnacle General Linear Model: >lm(w.wbar ~ Ht, data = height) Generalized Linear Model: >glm.height<-glm(Npartial/N~Ht,family=binomial,weights=N,data=height)) Odds Ratio: 1.26

19. Height of barnacle residuals plots LM GLM

20. Summary of model comparisons…GLM vs LM

21. Max Diameter General Linear Model: >lm(w.wbar ~ MaxDiam, data = maxdiam) Generalized Linear Model: >glm(Npartial/N ~ MaxDiam, family = binomial, data = maxdiam,weights = N) Odds Ratio: 1.073

22. Max Diameter residuals plots LM GLM

23. Summary of model comparisons…GLM vs LM

24. Okay, that’s it…