| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
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| Research Abstract |
The purpose of this project was to study the methods for analyzing longitudinal categorical data to quantify individuals' changes. We focused on an indicator matrix whose rows and columns associated with the individuals over time-points and with categories, respectively. From this data matrix, individual changes cannot be quantified by the existing quantification method, To deal with this difficulty, we developed constrained and regularized methods for quantification.
In the constrained method, the growth curve constraint is imposed on the scores to be assigned to the individuals over time-points : the scores is constrained to be a polynomial in time. The usefulness of this method we developed was shown by its application to real data. This method was further extended to simultaneously perform the clustering of individuals.
In the regularized method, the loss function in the existing method is combined with a penalty function, to form a penalized loss function. This method is subdivided into two approaches. One is to define the penalty using first order differences of scores, which requires the homogeneity of individual scores over time-points. The other is to treat the scores as natural cubic spline functions of time and to define the penalty using the second order derivative of the splines, assuming individual scores to change smoothly with time. Both methods gave promising results in simulation and real data analysis.
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