Post on 18-Dec-2015
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
PoissonBinomial
Negative BinomialGamma
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)Advantages
• Assumptions more evident• Decouples assumptions• Improves quality• Greater flexibility
Generalized Linear Model (GzLM)Advantages
• Assumptions more evident• Decouples assumptions• Improves quality• Greater flexibility
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=∑ (𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 )2𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑
χ2 = 0.3907df = 1p = 0.532
Classic Chi-square Statistic Example
Gregor Mendel’s Peas
• Deviation from genetic model (3:1) not significant