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I have had to include a squared term in my regression model due to observed non-linearity in the LOWESS plot.

In my reading to understand how to interpret the coefficients on the linear and squared term, most advice to centre around the mean. However, my model regression is multivariate, with linear variables.

I'm unsure whether to still mean centre, especially as all examples I've seen generally are measuring a bivariate relationship.

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A better approach for a curvilinear association between outcome and a continuous predictor is a regression spline or a different type of generalized additive model. Chapter 2 of Frank Harrell's Regression Modeling Strategies discusses regression splines.

Whether you keep to the quadratic fit or use a spline, the fundamental regression model will be the same whether or not you center the continuous predictors. Centering can sometimes prevent numerical fitting difficulties, and the coefficient estimates that you see might differ depending on centering. But predictions from the model will be the same regardless, and statistical tests that evaluate together all the coefficients associated with a predictor will also be the same.

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  • $\begingroup$ Thank you so much - just a follow-up question, if you have time. I think I may create a predicted value plot using the quadratic fit and then add a supplementary note from the regression spline results. For my theoretical framework, I believe I will have to lag my main independent variable - are there any specific considerations I should have considering it now has a linear and squared term? $\endgroup$
    – Tolu
    Apr 28, 2023 at 15:54
  • $\begingroup$ @Tolu the strengths and weaknesses of a simple polynomial versus a regression spline will be the same. The difficulty is that a model requiring lags typically involves some autocorrelation in outcomes over time. They thus can require specialized approaches to time-series data than can account for such autocorrelations. That's separate, however, from the choice between simple polynomial and regression spline. $\endgroup$
    – EdM
    Apr 28, 2023 at 16:26
  • $\begingroup$ that's introduced a new consideration for me and I've just ran the test and turns out I do have an issue of autocorrelation. From a brief reading, it seems fe robust/cluster commands can control for that and I can add this to my specification. I likely state my "IV in polynomial regression" question a little better here - stats.stackexchange.com/questions/614417/… $\endgroup$
    – Tolu
    Apr 28, 2023 at 17:04

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