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🔗 '''Interaction effect''' describes a statistical phenomenon in which the combined influence of two or more variables on an insurance outcome differs from what would be expected by simply adding their individual effects together. In [[Definition:Actuarial science | actuarial]] modeling and insurance [[Definition:Predictive analytics | predictive analytics]], interaction effects are everywhere: the impact of a driver's age on [[Definition:Motor insurance | auto claim]] [[Definition:Frequency | frequency]] might depend heavily on vehicle type, or the relationship between building age and [[Definition:Property insurance | property]] [[Definition:Severity | loss severity]] might vary dramatically by geographic zone and construction material. Capturing these joint effects is what allows a [[Definition:Rating algorithm | rating model]] to reflect reality rather than treating each risk factor as if it operates in isolation.

📐 In practice, analysts incorporate interaction effects by adding product terms or using flexible model architectures. A [[Definition:Logistic regression | logistic regression]] predicting [[Definition:Fraud | fraud]] probability might include an interaction between claim size and claimant history, reflecting the insight that large claims from first-time claimants carry a different fraud signal than large claims from policyholders with extensive tenure. [[Definition:Generalized linear model (GLM) | Generalized linear models]], the workhorses of insurance pricing across markets from the UK to Australia to Japan, routinely include carefully selected interaction terms identified through actuarial judgment and data exploration. More complex [[Definition:Machine learning | machine learning]] methods — gradient-boosted trees, neural networks — capture interactions automatically, though the trade-off is reduced interpretability, which can create challenges when regulators require transparent [[Definition:Rate filing | rate justifications]]. Under [[Definition:Solvency II | Solvency II]] in Europe and state-based regulatory frameworks in the United States, insurers must often demonstrate that the rating variables and their combinations used in pricing are actuarially justified and not unfairly discriminatory, making the documentation of interaction effects a compliance concern as well as a technical one.

💡 Overlooking meaningful interaction effects leads to [[Definition:Underwriting | underwriting]] models that systematically misprice certain segments. A health insurer that models age and smoking status only as independent main effects will underestimate the [[Definition:Loss ratio | loss cost]] for older smokers and overestimate it for younger smokers, creating [[Definition:Adverse selection | adverse selection]] vulnerabilities as competitors with better models cherry-pick the overcharged segments. For [[Definition:Reinsurance | reinsurers]] building [[Definition:Catastrophe model | catastrophe models]], the interaction between hazard intensity and local building codes can be the difference between an adequate and a dangerously optimistic [[Definition:Reserve | reserve]]. As the industry's analytical sophistication deepens — driven by richer [[Definition:Data | data]] sources and growing computational power — the ability to detect, validate, and explain interaction effects has become a hallmark of best-in-class pricing and [[Definition:Risk management | risk management]] practice.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Generalized linear model (GLM)]]
* [[Definition:Logistic regression]]
* [[Definition:Heterogeneous treatment effect]]
* [[Definition:Predictive analytics]]
* [[Definition:Risk classification]]
* [[Definition:Machine learning]]
{{Div col end}}

Definition:Interaction effect - Revision history

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