The model for each age tk,k = 1...131, is represented by the following equation, in which yij is the dependent variable for subject i at observation j at age tij, Wh(t) the kernel weighting for the local linear regression model, 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. Different sets of covariates may be used for the estimation of the slope and the intercept. The weight Wh(tij −tk) will be non-zero only for an interval near tk and diminishes rapidly as the distance between tij and tk increases. Note that the beta values are indexed to emphasize that each is the product of a separate estimation for each age. (In the equation, intercept terms appear on the first line and slope terms on the second line. The summations are over the repeated indices in the covariates and betas.) Wh(tij−tk)yij=Wh(tij−tk)[β0,0,k+∑Xi,j,nβ0,n,k+(β1,0,k+∑Xi,j,mβ1,m,k)∗(tij−tk)]
