# Detect Non-Linear and Non- Monotonic Relationship between Variables

In linear regression analysis, it's an important assumption that there should be a linear relationship between independent variable and dependent variable. Whereas, logistic regression assumes there should be a linear relationship between independent variable and logit function.

How to check non-linearity

Pearson correlation is a measure of linear relationship. The variables must be measured at interval scales. It is sensitive to outliers. If pearson correlation coefficient of a variable is close to 0, it means there is no linear relationship between variables.

Spearman's correlation is a measure of monotonic relationship. It can be used for ordinal variables. It is less sensitive to outliers. If spearman correlation coefficient of a variable is close to 0, it means there is no monotonic relationship between variables.

Hoeffding’s D correlation is a measure of linear, monotonic and non-monotonic relationship. It has values between –0.5 to 1. The signs of Hoeffding coefficient has no interpretation.
If a variable has a very low rank for Spearman (coefficient - close to 0) and a very high rank for Hoeffding indicates a non-monotonic relationship.
If a variable has a very low rank for Pearson (coefficient - close to 0) and a very high rank for Hoeffding indicates a non-linear relationship.

Criterion to eliminate irrelevant variables
If a variable has poor rank on both the spearman and hoeffding correlation metrics, it means the relationship between the variables is random.

SAS Macro to detect non-monotonic relationship
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Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 10 years of experience in data science. During his tenure, he has worked with global clients in various domains like Banking, Insurance, Private Equity, Telecom and Human Resource.

11 Responses to "Detect Non-Linear and Non- Monotonic Relationship between Variables"
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1. Spearman correlation measures monotonic relationship. When you say a variable having high spearman rank, i am assuming it's correlation value is high or moderate. It means the association is monotonic. Hope it helps.

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