Monotonic Regression

TL;DR

Enforces that the dependent variable either never decreases or never increases as the independent variable increases.
Useful when the direction (non-decreasing or non-increasing) of the relationship is known but the exact functional form is unknown.
Can be used to identify the underlying relationship and make predictions, but it may assume strict monotonicity and be computationally intensive.

Definition

Monotonic regression is a type of regression analysis that involves finding a non-decreasing or non-increasing relationship between a dependent variable and an independent variable. This means that the dependent variable will either always increase or always decrease as the independent variable increases.

Explanation

Monotonic regression constrains the fitted relationship so that it is either non-decreasing or non-increasing across the range of the independent variable. It is applied when the direction of change is known in advance but the precise functional form is unknown. By enforcing monotonicity, the method identifies an underlying relationship that can be used to make predictions about the dependent variable based on changes in the independent variable.

Examples

Age and height

As a person gets older, their height will typically increase until they reach their maximum height in their early 20s. After this point, their height will either remain constant or begin to decrease due to factors such as osteoporosis. In this case, the relationship between age and height is non-decreasing, or monotonically increasing.

Income and spending habits

As a person’s income increases, they may be more likely to spend more on luxury items such as clothing and electronics. However, as their income continues to increase, they may reach a point where they begin to save more money and spend less on non-essential items. In this case, the relationship between income and spending habits is non-increasing, or monotonically decreasing.

Use cases

Situations where the relationship between two variables is known to be non-decreasing or non-increasing but the exact functional form of the relationship is unknown.
Identifying an underlying monotonic relationship that can be used to make predictions about the dependent variable based on changes in the independent variable.

Notes or pitfalls

Monotonic regression assumes the relationship between the dependent and independent variables is strictly non-decreasing or non-increasing; in reality this may not always hold.
Other factors can influence the relationship (for example, in the relationship between age and height, factors such as genetics and lifestyle choices may also play a role in a person’s height).
Monotonic regression can be computationally intensive, particularly with large datasets or complex relationships.

Regression analysis
Dependent variable
Independent variable