Homogeneity and Smoothness Analysis for Quantifying a Longitudinal Categorical Variable
A variant of homogeneity analysis is proposed to analyze longitudinal data that describe the categories chosen by individuals at each of time-points. In the proposed method, individuals are given the scores that are natural cubic spline functions of time, and categories are given time-invariant scores. Loss of homogeneity between individual and category scores is combined with loss of smoothness of individual scores, to form a penalized loss function. It is minimized using eigenvalue or singular value decomposition. The weight of smoothness relative to homogeneity is chosen by a cross-validation procedure. The resulting scores yield a graphical representation of individuals’ trajectories with category points, which allows us to grasp longitudinal changes in individuals.
KeywordsPenalty Function Spline Function Correct Classification Rate Optimal Scaling Category Point
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