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In a traditional spline model, change points are generally selected as a whole number such as Time=2 because researcher designates a change at the time for examining an effect of an intervention or estimates known change points by expecting a change of growth. In this study, a piecewise growth mixture model (PGMM) will be discussed, which can estimate unknown change points including the form of decimal points. Furthermore, this study examines the efficient estimation method between Bayesian and maximum likelihood estimates within the PGM framework through a simulation study. In addition to the contribution via this study results, our future study is to develop a package from R that can be used with multiple change points within the mixture framework.