Piecewise Regression
In data analysis, breakpoints serve as crucial markers, indicating shifts in trends and behaviors that demand specialized modeling approaches.
Piecewise regression, often referred to as segmented regression or broken-stick regression, is a statistical technique that partitions a feature into intervals, fitting a separate line segment to each interval. The points that delineate these segments are known as breakpoints or knots. This approach provides greater flexibility in modeling relationships that may change at different levels of an independent variable.
Types of Piecewise Regression
- Piecewise Linear Regression
- Piecewise Polynomial Regression
- Spline Regression
- Cubic Spline Regression
- B-Spline Regression
- Threshold Regression
Piecewise Linear Regression
Piecewise linear regression is a statistical method that decomposes a nonlinear relationship into several linear segments. In this approach, the independent variable is divided into segments at specified breakpoints (knots), and a separate linear model is fitted to each segment. This technique is particularly useful when the independent features exhibit distinct relationships with the dependent variable across different groups.
Example: Consider a scenario in which a company increases an employee’s salary by $10,000 each year until the employee reaches the age of 40. After that age, the salary remains fixed, demonstrating a clear change in the relationship based on the age of the employee.
Let’s examine a visualization of the segmented data to illustrate how breakpoints affect the relationships between variables.
Comparison of models
Piecewise regression is particularly effective for specific types of data that exhibit clear breakpoints or changes in behavior. Such datasets often require tailored modeling approaches to accurately capture the underlying relationships between variables. In the example data presented, we demonstrate the effectiveness of piecewise regression by fitting three different models: linear regression, polynomial regression, and piecewise linear regression.
Conclusion
In conclusion, piecewise regression is a powerful tool for modeling data with breakpoints, as demonstrated in our analysis. The contrasting performances of linear, polynomial, and piecewise linear regression models underscore the importance of selecting appropriate modeling techniques based on the characteristics of the data. For datasets exhibiting distinct changes in relationships, piecewise regression stands out as the most suitable approach, delivering superior accuracy and insights.
Piecewise regression analysis can also be performed on multivariate data by partitioning the various independent variables. piecewise regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.
