Generalized linear models (GLM) relax the assumptions of standard linear regression. In particular, there are GLMs that can be used to predict discrete outcomes and model continuous outcomes with non-constant variance. In the era of sophisticated machine learning predictors, linear models have somewhat fallen out of favor, but they're still very useful in situations where there is little data, prediction is not the inferential goal, or speed is of paramount importance.
Recommended Books
An Introduction to Generalized Linear Models
Annette J. Dobson And Adrian G. Barnett
Key Features
- In-text exercises
- R and WinBUGS code examples
Key Topics
- Analysis of Variance/Covariance
- Bayesian Analysis
- Clustered and Longitudinal Data
- Collinearity
- Diagnostics
- Exponential Family Distributions
- Goodness of Fit Statistics
- Hypothesis Testing
- Inference
- Log-Linear Models
- Logistic Regression
- Markov Chain Monte Carlo Methods
- Maximum Likelihood Estimation
- Model Fitting
- Multiple Linear Regression
- Normal Linear Models
- Normal and Related Distributions
- Ordinal Logistic Regression
- Poisson Regression
- Repeated Measures Models
- Survival Analysis
Description
This is our go-to book for GLM. The text includes a good review of linear models based on the normal distribution, model fitting, logistic regression and Poisson regression, as well as some bonus topics such as survival analysis. Our favorite part is that there is a full-fledged Bayesian treatment of some GLMs. This book is fairly mathematical for an introduction to an applied topic, but it is very readable.
Foundations of Linear and Generalized Linear Models
Alan Agresti
Key Features
- In-text exercises
- Some exercise solutions
- R example code
Key Topics
- Bayesian Linear Modeling
- Binary Data Modeling
- Confidence Intervals and Prediction Intervals
- Correlated Responses
- Exponential Family Distributions
- Hypothesis Testing
- Inference
- Least Squares Model Fitting
- Logistic Regression
- Models for Count Data
- Negative Binomial Regression
- Nominal Response Models
- Normal Linear Models
- Ordinal Response Models
- Poisson Regression
- Probit Regression
- Quasi-Likelihood Methods
- Residuals, Leverage, and Influence
- Robust Regression
Description
This is a gentler book on GLMs than our main pick. Agresti is a great author (he has written several other excellent statistics books as well), and this book is a great overview of linear and generalized linear models. It doesn't have the same coverage as Dobson and Barnett (in particular, it doesn't have the same amount of Bayesian material), but it does have solutions to some exercises, which makes it great for the autodidact.
