The model for each central age tk, k = 1 … 131, is represented by the following equation, in which yi, j is the dependent variable for subject i at observation j at age ti, j, Wh(t) the value of weighting function for the local linear regression model at age distance t from the central age, a function of the bandwidth (fraction of data included) h, β0,n,k the parameter to be estimated for covariate n for its effect on the intercept and β1,n,k the parameter to be estimated for covariate n for its effect on the slope, and Xi, j,m the value of covariate m of subject i at observation j and ei, j the error term. Different sets of covariates may be used for the estimation of the slope and the intercept. The weight Wh(ti, j − tk) will be non-zero only for an interval near tk and diminishes rapidly as the distance between ti, j and tk increases. Note that the beta values are indexed to emphasize that each is the product of a separate estimation for each
