[burger]

Obviously, I am making fun of reducing a continuous predictor into a bunch of categories.  Your point is well taken, but, more importantly, you don't have to preserve the degrees of freedom; a quick perusal of the data would tell you that a simple quadratic is probably a better descriptor of the data, and it has saved you three DF's.

And/but, as always, it depends on what you want to do with the results.  An nth degree polynomial (where n > 1) makes it hard to explain what is seen, since the terms higher than the linear term are hard to describe, unless they are all positive.  More importantly, while as a 44-year-old, it is pretty easy to look at my risk category and infer that I would likely be at the upper end of the range for the 18-44 year old category, while more precise, it would be much harder to calculate my risk with even a quadratic polynomial, absent a calculator.  So there is a tradeoff between precision and ease of understanding.

BC

I know you were being tongue in cheek. I was, too, sort of.

If I was doing this for publication, I'd try to get a more parsimonious model by 1) running polynomials of various degrees and comparing likelihoods, etc. or 2) using penalized splines.

And making it understandable to the public is easy.  Just make the r or matlab code available at github, and then anyone who's interested can download the data and run the models themselves.  Doesn't everyone know how to run a polynomial regression nowadays? ;)

[burger]

Obviously, I am making fun of reducing a continuous predictor into a bunch of categories.  Your point is well taken, but, more importantly, you don't have to preserve the degrees of freedom; a quick perusal of the data would tell you that a simple quadratic is probably a better descriptor of the data, and it has saved you three DF's.

And/but, as always, it depends on what you want to do with the results.  An nth degree polynomial (where n > 1) makes it hard to explain what is seen, since the terms higher than the linear term are hard to describe, unless they are all positive.  More importantly, while as a 44-year-old, it is pretty easy to look at my risk category and infer that I would likely be at the upper end of the range for the 18-44 year old category, while more precise, it would be much harder to calculate my risk with even a quadratic polynomial, absent a calculator.  So there is a tradeoff between precision and ease of understanding.

BC

I know you were being tongue in cheek. I was, too, sort of.

If I was doing this for publication, I'd try to get a more parsimonious model by 1) running polynomials of various degrees and comparing likelihoods, etc. or 2) using penalized splines.

And making it understandable to the public is easy.  Just make the r or matlab code available at github, and then anyone who's interested can download the data and run the models themselves.  Doesn't everyone know how to run a polynomial regression nowadays? ;)