1. Part V The Generalized Linear Model Chapter 16 Introduction

2. t-test ANOVA Simple Linear Regression Multiple Linear Regression ANCOVA GENERAL LINEAR MODELS ε ~ Normal R: lm()

3. t-test ANOVA Simple Linear Regression Multiple Linear Regression ANCOVA Poisson Binomial Negative Binomial Gamma Multinomial GENERALIZED LINEAR MODELS Inverse Gaussian Exponential GENERAL LINEAR MODELS ε ~ Normal Linear combination of parameters R: lm() R: glm()

4. Generalized Linear Model (GzLM) Introduction Assumptions of GLM not always met using biological data

5. Generalized Linear Model (GzLM) Introduction

7. Assumptions of GLM not always met using biological data – Transformations typically recommended – We can randomize… Assumes parameter estimates (means, slopes, etc.) are correct – But a few large counts or many zeros will influence skew our estimates

8. Generalized Linear Model (GzLM) Introduction

10. Assumptions of GLM not always met using biological data – Transformations typically recommended – We can randomize… Assumes parameter estimates (means, slopes, etc.) are correct – But a few large counts or many zeros will influence skew our estimates – Best to use an appropriate error structure under the Generalized Linear Model framework

11. Generalized Linear Model (GzLM) Introduction Poisson error structure

12. Generalized Linear Model (GzLM) Introduction Binomial error structure

13. Generalized Linear Model (GzLM) Advantages Assumptions more evident Decouples assumptions Improves quality Greater flexibility

14. Generalized Linear Model (GzLM) Advantages Assumptions more evident Decouples assumptions Improves quality Greater flexibility

15. Part V The Generalized Linear Model Chapter 16.1 Goodness of Fit

16. Goodness of Fit - The Chi-square statistic Have to learn a new concept to apply GzLM: – Goodness of Fit Chi-square statistic G-statistic

17. Classic Chi-square Statistic Example Gregor Mendel’s Peas Purple: White:

18. χ 2 = 0.3907 df = 1 p = 0.532 Classic Chi-square Statistic Example Gregor Mendel’s Peas

19. χ 2 = 0.3907 df = 1 p = 0.532 Classic Chi-square Statistic Example Gregor Mendel’s Peas Deviation from genetic model (3:1) not significant

20. Goodness of Fit - The G-statistic Can deal with complex models Based in likelihood

21. Goodness of Fit - The G-statistic Smaller deviation  smaller G-statistic G-statistic   p-value = 0.53

22. Improvement in Fit - ΔG Next time we will… – Compare G values (ΔG) to assess improvement in fit of one model over another