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I am to analyze a set of economic variables, taken from multiple countries, and recorded across time. This is certainly a panel dataset.

If I'm not mistaken, the pooled OLS, fixed and random effects models are linear

random effects model

while polynomial regression models seem to focus on a single variable

polynomial regression

Is there such a thing as a polynomial panel regression model? I am having a very hard time finding any explanation online or in textbooks about this particular topic.

Thank you in advance for any help, all possible indications as to where to learn about this topic are welcome.

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1 Answer 1

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Adding polynomial terms may help at capturing possible non-linear effects in the covariates, thus you can add such terms in a random-effects model just as you do in the classical linear regression. There may be tons of examples of applications using polynomial terms in a random-effects model, one that I can recall right now is Pinheiro and Bates (2000) Mixed-Effects Models in S and S-Plus, Springer, Sect. 1.5.

With random-effects models, you could even estimate more complicated nonlinear relationships between a response and a covariate; the details with an R implementation can be found in the aforementioned book, in Chapters 6, 7 and 8.

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    $\begingroup$ Thank you very much for your timely response. The R implementation will surely help me with my project. $\endgroup$
    – andrés
    Apr 6, 2023 at 20:25

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