ABSTRACT
This chapter describes some options and factors involved in choosing a functional form with a focus on one particularly good option: higher-order polynomials. It discusses the three major considerations involved in choosing a functional form for the kinds of data we typically encounter in the behavioral sciences. Using higher-order polynomials requires choosing the specific order of the polynomial to be used for each analysis. A theoretical approach takes the complementary view: the model should include only those terms for which the experimenter predicted an effect. For higher-order polynomials, the individual time terms tend to be correlated. Natural and orthogonal polynomial terms have the same shapes, but the centering of orthogonal polynomials gives them slightly different interpretations compared to natural polynomials. To interpret polynomial effects in the context of complex data shapes it can be useful to think of each term as a separate component for the observed data curve.
