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Multivariate adaptive splines for analyzing longitudinal data

An essential feature of longitudinal data is the existence of correlation among the observations from the same unit of observation such as a patient. Two-stage random-effect linear models are commonly used to analyze longitudinal data. These models are, however, not flexible enough for exploring the underlying data structures and, especially, for describing time trends. Various semi-parametric models exist to accommodate general time trends. But, these semi-parametric models do not provide a convenient way to explore interactions among time and other covariates although such interactions exist in many applications. Moreover, semi-parametric models require specifying the design matrix of the covariates (time excluded). Multivariate adaptive splines for analyzing longitudinal data (MASAL) offer a nonparametric method to resolve these issues. To fit nonparametric models, MASAL uses the multivariate adaptive regression splines for the estimation of mean curve and then apply an EM-like iterative procedure for covariance estimation. I will demonstrate the use of MASAL with both simulated and real data.