Limitations of linear models

Generalized Linear Models in R

Richard Erickson

Instructor

Course overview

Chapter 1: Review and limits of linear model and Poisson regressions
Chapter 2: Logistic (Binomial) regression
Chapter 3: Interpreting and plotting GLMs
Chapter 4: Multiple regression with GLMs

Workhorse of data science

Linear modes: Workhorse of data science

¹ US Department of Agriculture https://www.nal.usda.gov/exhibits/ipd/localfoods/exhibits/show/farmto–table/the–roads–of–rural–america

Linear models

How can linear coefficients explain the data?
Intercept for baseline effect
Slope for linear predictor
$y = \beta_0 + \beta_1 x + \epsilon $

Linear models in R

lm(y ~ x, data = dat)

Assumption of linearity

Example of linear and non-linear data

Assumption of normality

Normal vs non-normal residuals

Assumption of continuous variables

Continuous compared to non-continuous data .

Boxplot of chick weights at end of study

Chick diets impact on weight

ChickWeight data from datasets package
ChickWeightsEnd last observation from study
How do diets 2, 3, and 4 compare to diet 1?

lm(formula = weight ~ Diet, data = ChickWeightEnd)

    Call:
    lm(formula = weight ~ Diet, data = ChickWeightEnd)
    Coefficients:
    (Intercept)        Diet2        Diet3        Diet4  
         177.75        36.95        92.55        60.81

What about survivorship or counts?

What about chick survivorship or chick counts?
Neither are continuous!
We need a new tool
The generalized linear model

Generalized linear model

Similar to linear models
Non-normal error distribution
Link functions: $y = \psi(b_0 + b_1 x + \epsilon)$

GLMs in R

glm( y ~ x, data = data, family = "gaussian")

lm() same as glm( ..., family = "gaussian")

Let's practice!!

Generalized Linear Models in R