An efficient method to estimate some statistical models has been proposed and developed for the longitudinal data under the settings of Local Box-Cox transformation (LBCT).Box-Cox Transformation (BCT) is usually used on cross-sectional data for normality approximation. For longitudinal data, BCT is irrelevant. In this paper, instead of BCT, we develop LBCT, and will use it after splitting the longitudinal data by time (age) variable. The longitudinal data is split in such way that the repeated measurements for each subject exist across different time points, but within a time point no repeated measurements exist. By doing this, longitudinal data turns into a set of time-variant cross-sectional data, and normality on variable of interest for each split data is achieved. Our estimation is based on three steps. First, we split the data. We then apply LBCT on each data in second step, and in third step, we accomplish efficient estimation of our models by incorporating three nonparametric smoothers, known as local polynomial smoother, kernel smoother and spline smoother so that the models can be estimated on entire time range. Application and simulation of our methods will be shown.