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Part V The Generalized Linear Model

Part V The Generalized Linear Model. Chapter 16 Introduction. GENERAL LINEAR MODELS. ε ~ Normal. R: lm(). ANOVA. Multiple Linear Regression. t-test. Simple Linear Regression. ANCOVA. GENERALIZED LINEAR MODELS. Linear combination of parameters . R: glm(). Multinomial. Binomial.

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Part V The Generalized Linear Model

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  1. Part VThe Generalized Linear Model Chapter 16 Introduction

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

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

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

  5. Generalized Linear Model (GzLM)Introduction

  6. Generalized Linear Model (GzLM)Introduction

  7. 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

  8. Generalized Linear Model (GzLM)Introduction

  9. Generalized Linear Model (GzLM)Introduction

  10. 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

  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 VThe 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 ExampleGregor Mendel’s Peas Purple: White:

  18. Classic Chi-square Statistic ExampleGregor Mendel’s Peas χ2 = 0.3907 df = 1 p = 0.532

  19. Classic Chi-square Statistic ExampleGregor Mendel’s Peas • Deviation from genetic model (3:1) not significant χ2 = 0.3907 df = 1 p = 0.532

  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

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