What are Generalized Linear Models (GLMs), Linear Models, and Mixed Models, and how do they differ from each other?

Answered on : 2024-01-23

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Generalized, Linear, and Mixed Models, 2nd Edition

wiley.com

Generalized, Linear, and Mixed Models

onlinelibrary.wiley.com

Generalized, Linear, and Mixed Models, 2nd Edition: ...

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1. **Generalized Linear Models (GLMs):**

- GLMs extend traditional linear models by accommodating non-normally distributed response variables, using a link function and a probability distribution [6].

- Notable for addressing various data types, such as binary or count data [10].

2. **Linear Models:**

- Traditional linear models assume a linear relationship between predictors and the response variable, suitable for normally distributed data [4].

3. **Mixed Models:**

- Extend linear models to account for both fixed and random effects, capturing variability in data not explained by fixed effects alone [4].

- Useful for handling correlated observations and hierarchical structures in data [6].

These models share foundational concepts but serve distinct purposes, allowing statisticians to address a wide range of data scenarios effectively. Understanding their similarities and differences is crucial for appropriate model selection and interpretation.