If the instantaneous state of the developmental process is represented as g(t), then the measured cumulative value (developmental trajectory) s(t) equals ∫t0tg(x)dx. In order to obtain the developmental rate curve (velocity curve) g(t) the time derivative of s(t) must be estimated. Since there is no explicit biological model for the development process, no parametric form is attributed to g(t) or s(t). In the varying coefficient model (Fan and Zhang, 2008) used in this study, the dependent variable, a point on the developmental trajectory, is an implicit (non-parametric) function of age, and the effects of the independent variables (covariates) on the developmental trajectory can vary with age. (In this study, the developmental trajectories are those of the natural logarithm of theta ERO power values from the scalp locations mentioned above. The logarithmic transformation of the data was used to eliminate the skewed distribution found at every age. In the paper all uses of the word “log” as short for “logarithm” mean natural logarithm, including all text on figures.) The mean of the developmental trajectory s(t) and its time derivative is estimated
