Generalized Additive Models
- Flexible regression models that allow non-linear relationships between predictors and the response.
- Use smooth functions (“smooths”) to capture those non-linear effects instead of assuming linearity.
- Often produce more accurate fits than simple linear regression when relationships are not linear.
Definition
Section titled “Definition”Generalized Additive Models (GAMs) are a type of regression model that allows for the incorporation of non-linear relationships between the response variable and predictor variables. This is achieved through the use of smooth functions, known as “smooths”, which capture the non-linear relationship between the response and predictor variables.
Explanation
Section titled “Explanation”GAMs replace the strict linear relationship assumed by ordinary linear regression with flexible smooth functions for one or more predictors. Each smooth function models how a predictor relates to the response without forcing a linear form, enabling the model to follow non-linear patterns present in the data. By doing so, GAMs can produce more accurate representations of relationships where linearity does not hold.
Examples
Section titled “Examples”Temperature and ice cream sales
Section titled “Temperature and ice cream sales”In this scenario, the response variable is the number of ice cream sales and the predictor variable is the temperature. A linear regression model would assume that the relationship between temperature and ice cream sales is linear, but this may not accurately capture the relationship in reality. A GAM would instead use a smooth function to capture the non-linear relationship between temperature and ice cream sales, resulting in a more accurate model.
Age and blood pressure
Section titled “Age and blood pressure”In this scenario, the response variable is the blood pressure and the predictor variable is the age. A linear regression model would assume that the relationship between age and blood pressure is linear, but this may not accurately capture the relationship in reality. A GAM would instead use a smooth function to capture the non-linear relationship between age and blood pressure, resulting in a more accurate model.
Use cases
Section titled “Use cases”- Analyzing the relationship between environmental factors and plant growth.
- Studying the relationship between diet and health outcomes.
Related terms
Section titled “Related terms”- Smooths (smooth functions)
- Linear regression
- Regression model