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Some scholars test for curvilinear (U or inverted U shaped) relationship in nonlinear models such as Poisson and negative binomial.

  1. Isn't the relationship between a predictor and a response by definition curvilinear in a non-linear model such as Poisson?

  2. Does the significance of a quadratic term of the corresponding predictor in the Poisson model validate the existence of a U or inverted U in the same way as the significance of quadratic terms in the case of OLS? What are the differences?

Ferdi
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Pankaj Kumar
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  • Please explain what you mean by the "Poisson model" and what you mean by it being "nonlinear." In case I sound a little obscure, note the many different possible meanings of "nonlinear" discussed at http://stats.stackexchange.com/questions/148638. – whuber Jul 01 '16 at 17:44
  • Thanks! By nonlinear models I mean the models that are nonlinear in parameters. Poisson model is a model that assumes that counts are Poisson distributed. But more generally models of the form y = e^(alpha x + beta x^2) in contrast to the ols y= alpha x + beta x^2 – Pankaj Kumar Jul 01 '16 at 18:02

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