Abstract
The multilevel growth curve has long been a staple of longitudinal data analysis. In the model there is, however, one parameter that can present interpretive difficulties; namely, the correlation between the individuals’ level and the individuals’ shape. The tendency to place an interpretive value on this parameter typically comes from the desire to make a statement such as “the relationship between the individual’s initial level and the resulting trajectory is strong.” In this paper we show first the algebraic relationship between the level and shape parameters for the linear version of the growth curve model. We next show how and why the correlation is strongly affected by the placement of the intercept. By repositioning the intercept, we can essentially determine the size and direction of the correlation. Using a ‘pick-up-sticks model’, we describe why trying to interpret the association between level and shape can cause difficulties. Given these results, we show that the interpretation of correlation is most difficult when the process we measure is not at its true beginning. In the case where we begin measurements in the midst of a growth process, the correlation will be affected by where in the process we begin the measurement. As a result, our best chance for an interpretable parameter comes when we begin measurements at the true beginning of a process. We show these relationships and their implications both with simulated data and with data taken from the gerontological literature.