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Today: Lab 9ab due after lecture: CEQ Monday: Quizz 11: review

DEC 8 – 9am FINAL EXAM EN 2007. Today: Lab 9ab due after lecture: CEQ Monday: Quizz 11: review Wednesday: Guest lecture – Multivariate Analysis Friday: last lecture: review – Bring questions. Biology 4605 / 7220 Name ________________ Quiz #10a 19 November 2012

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Today: Lab 9ab due after lecture: CEQ Monday: Quizz 11: review

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  1. DEC 8 – 9am FINAL EXAMEN 2007 Today: Lab 9ab due after lecture: CEQ Monday: Quizz 11: review Wednesday: Guest lecture – Multivariate Analysis Friday: last lecture: review – Bring questions

  2. Biology 4605 / 7220 Name ________________ • Quiz #10a 19 November 2012 • What are the 2 main differences between general linear models and generalized linear models? • 2. A generalized linear model links a response variable to one or more explanatory variables Xi according to a link function.

  3. Biology 4605 / 7220 Name ________________ • Quiz #10a 19 November 2012 • What are the 2 main differences between general linear models and generalized linear models? • Most common answers: • A. Non –normal ε • B. ANODEV instead of ANOVA table • C. Link function • 2. A generalized linear model links a response variable to one or more explanatory variables Xi according to a link function. implementation conceptual

  4. GLM, GzLM, GAMA few concepts and ideas

  5. GLM Model based statistics – we define the response and the explanatory without worrying about the name of the test

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

  7. GLM An example from Lab 9

  8. GLM Do fumigants (treatments) decrease the number of wire worms? #ww = β0 + βtreatment treatment + βrow row + βcolumn column treatment  fixed row  random column  random N=25

  9. GLM N=25

  10. GLM N=25

  11. GLM N=25

  12. GLM N=25

  13. GLM p-value borderline Normality assumption not met

  14. GLM p-value borderline Normality assumption not met n<30 Given that we do not violate the homogeneity assumption, randomizing will likely not change our decision… or will it? Let’s try  prand = 0.0626 (50 000 randomizations) N=25

  15. GLM Parameters: Means with 95% CI Anything wrong with this analysis?

  16. GLM Response variable? Counts

  17. GzLMPoisson error #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column

  18. GzLMPoisson error #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column ALL fits > 0

  19. GzLMPoisson error

  20. GzLMPoisson error

  21. 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 GzLM

  22. GzLM #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column Generalized linear models have 3 components: Systematic Random Link function

  23. GzLM #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column Generalized linear models have 3 components: Systematic linear predictor Random Link function

  24. GzLM #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column Generalized linear models have 3 components: Systematic linear predictor Random probability distribution  poisson error Link function

  25. GzLM #ww = eμ+ ε μ = β0 + βtreatment treatment + βrow row + βcolumn column Generalized linear models have 3 components: Systematic linear predictor Random probability distribution  poisson error Link function log

  26. GzLM

  27. GLM An example from Lab 6

  28. GLM Do movements of juvenile cod depend on time of day? distance = β0 + βperiod period period  categorical

  29. GLM

  30. GLM Anything wrong with this analysis?

  31. GAM

  32. GENERALIZED ADDITIVE MODELS R: gam() GENERALIZED LINEAR MODELS Linear combination of parameters R: glm() Non-linear effect of covariates 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 GAM

  33. GAM Generalized case of generalized linear models where the systematic component is not necessarily linear distance ~ s(period) y ~ s(x1) + s(x2) + x3 + …. s: smooth function Spline functions are concerned with good approximation of functions over the whole of a region, and behave in a stable manner

  34. GAM Smoothing - concept

  35. GAM How much smoothing? - + Degree of smoothness

  36. GAM

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

  38. GENERALIZED LINEAR MODELS Non-normal ε Link function 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

  39. Linear predictor involves sums of smooth functions of covariates GENERALIZED ADDITIVE MODELS R: gam() GENERALIZED LINEAR MODELS Linear combination of parameters R: glm() Non-linear effect of covariates 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

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