#Quadratic polynomial example how to#

Appendix A provides a brief description of how orthogonal polynomials are expressed and derived. All of those methods are generated from the same rationale about orthogonality of polynomials. There is a variety of approaches to express orthogonal polynomials, such as the Hermite, the Chebyshev, and the Legendre polynomials. Which can be expanded to determine all П• ~ k T j. Given the application of centering on T, the two time polynomial terms are no longer highly correlated. If T is rescaled to be centered at time 1, then T takes values в€’1, 0, and 1 at the three time points, respectively, instead of 0, 1, and 2 correspondingly, T Г— T will take values 1, 0, and 1. Centering T at a selected value provides an appropriate solution for reducing high collinearity between the two time polynomials. In this case, the direct specification of the quadratic function can significantly affect the estimation of the model parameters. Obviously, those two time components are almost perfectly correlated. Correspondingly, the second-order polynomial is scaled as 0, 1, and 4. Suppose that the quadratic polynomial function is used to describe the pattern of change in Y over three time points, where T is scaled as 0, 1, and 2, respectively.

A simple example in this regard is provided in Hedeker and Gibbons (2006).

#Quadratic polynomial example how to#

Given high correlation among the linear, quadratic, and high-order polynomial terms, the researcher must consider how to reduce collinearity in using various polynomial time functions. Xian Liu, in Methods and Applications of Longitudinal Data Analysis, 2016 3.4.2 Methods to reduce collinearity in polynomial time termsДЄlthough the quadratic polynomial function is very flexible, some high-order polynomial functions are occasionally used to describe irregularly shaped patterns of change over time.