In growth-curve modeling, how is time used to test higher-order trends?

• A. Include time raised to the order of the polynomial.
• B. Use time as a binary category.
• C. Time as a logarithm of time.
• D. Exclude time and use other predictors.

Answer: (A)

In growth-curve modeling, higher-order trends are tested by adding polynomial terms of time to the model. This means you include time raised to increasing powers—time, time squared, time cubed, and so on. Each additional power lets the model fit more complex, curved trajectories rather than a straight line. If the coefficient on a higher-order time term is significant, that indicates a nonlinear pattern at that level of curvature (quadratic for time^2, cubic for time^3, etc.). To keep the estimates stable and interpretable, time is often centered before creating these polynomial terms, which reduces multicollinearity between time and its powers.

This approach differs from treating time as a binary category, which would only compare outcomes at distinct time points rather than modeling a smooth growth path, or from using a transformed time like a logarithm, which imposes a specific nonlinear form that’s not the same as a polynomial trend. Excluding time altogether would miss the fundamental growth process being studied.