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Caitlyn Donadt & Morganne Wall
The Problem with Linear
Assumptions
1. Normality
2. Homogeneity
3. Fixed X
4. Independence
5. Correct Model Specification Model Validation
> op <- par(mfrow = c(2, 2), mar = c(5, 4, 1, 2))
#specifies a graphing window with 4 panels
> plot(Model1, add.smooth = FALSE, which = 1)
> E <- resid(M1)
> hist(E, xlab = "Residuals", main = "")
> plot(Dataset$Length, E, xlab = "Log(Length)", ylab =
"Residuals")
> plot(Dataset$Month, E, xlab = "Month", ylab =
"Residuals")
> par(op)
Figure 2.7 from Zuur 2009 using the Clams dataset available with the textbook...
Ecological Considerations
The world is not always normal
Poisson Distribution
Negative Binomial Distribution
Gamma Distribution
Infinite number of
What is a
Model Random Link
Systematic
Type
Linear
Regression
Normal Identity Continuous General
Linear
Model
ANOVA Normal Identity Categorical General
Linear
Model
ANCOVA Normal Identity Mixed General
Linear
Model
Logistic
Regression
Binomial Logit Mixed Generalized
Linear
Model
Loglinear Poisson Log Categorical Generalized
Linear
Model
Poisson
Regression
Poisson Log Mixed Generalized
Linear
Model
Note: modified from 6.1 Introduction to Generalized Linear
Models, buy The Pennsylvania State University, retrieved from
https://onlinecourses.science.psu.edu/stat504/node/216
Copyright 2018 by The Pennsylvania State University
What is a
Model Random Link
Systematic
Type
Linear
Regression
Normal Identity Continuous General
Linear
Model
ANOVA Normal Identity Categorical General
Linear
Model
ANCOVA Normal Identity Mixed General
Linear
Model
Logistic
Regression
Binomial Logit Mixed Generalized
Linear
Model
Loglinear Poisson Log Categorical Generalized
Linear
Model
Poisson
Regression
Poisson Log Mixed Generalized
Linear
Model
Note: modified from 6.1 Introduction to Generalized Linear
Models, buy The Pennsylvania State University, retrieved from
https://onlinecourses.science.psu.edu/stat504/node/216
Copyright 2018 by The Pennsylvania State University
What is a
Model Random Link
Systematic
Type
Linear
Regression
Normal Identity Continuous General
Linear
Model
ANOVA Normal Identity Categorical General
Linear
Model
ANCOVA Normal Identity Mixed General
Linear
Model
Logistic
Regression
Binomial Logit Mixed Generalized
Linear
Model
Loglinear Poisson Log Categorical Generalized
Linear
Model
Poisson
Regression
Poisson Log Mixed Generalized
Linear
Model
Note: modified from 6.1 Introduction to Generalized Linear
Models, buy The Pennsylvania State University, retrieved from
https://onlinecourses.science.psu.edu/stat504/node/216
Copyright 2018 by The Pennsylvania State University
GLM = Random component + systematic component + link function
Random component
0
1x
1
2x
2
0 1x
1 2x
22 2Systematic component
simple linear regression:
0
1xi
loglinear model:
Link function
An example of GLM model notation
Yi i)
We are using poisson distribution for
our random component
E(Yi i and var(Yi i
i) = × D.PARKi
Link Systematic component
Model Random Link
Systematic
Type
Logistic Regression Binomial Logit Mixed Generalized
Linear Model
Loglinear Poisson Log Categorical Generalized
Linear Model
Poisson Regression Poisson Log Mixed Generalized
Linear Model
Note: modified from 6.1 Introduction to Generalized Linear Models, buy The Pennsylvania State University, retrieved from
https://onlinecourses.science.psu.edu/stat504/node/216
Copyright 2018 by The Pennsylvania State University
References
personal communication, January 8 2018).
The Pennsylvania State University (2008). Lesson 7: GLM and
Poisson Regression. Retrieved from
http://personal.psu.edu/abs12//stat504/online/07_poisson/02_poi
sson_beyond.htm
The Pennsylvania State University (2018).
6.1 - Introduction to Generalized Linear Models. Retrieved from
https://onlinecourses.science.psu.edu/stat504/node/216 March
26, 2018
Zuur A. F. (2009). Mixed effects models and extensions in
Ecology with R.
