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Do You Even Data

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Reexamining the Effect of Income

A Comparison between Linear and Nonlinear Models

Market researchers frequently use linear regression models to perform critical analyses. These models examine how a predictor, such as a sudden increase in income, may determine an outcome, such as the likelihood that someone will donate to charity. Some sophisticated models even include interactions that show how the relationship between a predictor and and outcome vary over some key feature such as a customer’s annual salary.

Linear Model

The problem with this approach is that the relationship between a predictor and an outcome is assumed to be linear. Customer behavior is not always that simple. By using nonlinear models[1],[2] it is possible to gain a more accurate picture of whether someone will donate to charity after a sudden increase in their salary.

Nonlinear Model

A comparison between the two models reveals how linear models may conceal valuable information. Nonlinear models help you hear the voice of the customer more clearly. Sometimes the information the model reveals might be counter intuitive, such as the v-shape that shows those making around $75000 per year seem to be less generous to charity than those we both less and more money.

Model Comparison 2

Models like these can be used to help your business thrive by giving you more accurate insights into your business or marketing campaigns. You can always find out more about how nonlinear models - among several others - can help your business. There are many different ways to analyze the data, and we all seek to find the most nuance we possibly can.  

Who knows what valuable secrets lie hidden in the data?

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[1] Hastie T, Tibshirani R. Varying-coefficient models. Journal of the Royal Statistical Society, Series B. 1993; 55:757–779.

[2] Hoover DR, Rice JA, Wu CO, Yang LP. Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika. 1998; 85:809–822.