Abstract
Growth models (GM) of the mixed-effects and latent curve varieties have become popular
methodological tools in lifespan research. One of the major advantages of GM is their
flexibility in studying individual differences in change. We scrutinized the change functions
of GM used in five years of publications on cognitive aging. Of the 162 publications that we
identified, 88% test linear or quadratic polynomials, and fewer than 5% apply functions that
are nonlinear in their parameters, such as exponential decline. This apparent bias in favor of
polynomial decomposition calls for exploring what conclusions about individual differences
in change are likely to be drawn if one applies linear or quadratic GMs to data simulated
under a conceptually and empirically plausible model of exponential cognitive decline from
adulthood to old age. Hence, we set up a simulation that manipulated the rate of exponential
decline, measurement reliability, number of occasions, interval width, and sample size. True
rate of decline and interval width influenced results strongly, number of occasions and
measurement reliability exerted a moderate effect, and the effects of sample size appeared
relatively minor. Critically, our results show that fit statistics generally do not differentiate
misspecified linear or quadratic models from the true exponential model. Moreover, power to
detect variance in change for the linear and quadratic GMs is low, and estimates of individual differences in level and change can be highly biased by model misspecification. We
encourage researchers to also consider plausible nonlinear change functions when studying
behavioral development across the lifespan.
