Part V The Generalized Linear Model Chapter 16 Introduction

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

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()

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

Generalized Linear Model (GzLM) Introduction

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

Generalized Linear Model (GzLM) Introduction

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

Generalized Linear Model (GzLM) Introduction Poisson error structure

Generalized Linear Model (GzLM) Introduction Binomial error structure

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

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

Part V The Generalized Linear Model Chapter 16.1 Goodness of Fit

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

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

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

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

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

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

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