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Studies on Multidimensional Analysis of Longitudinal Categorical Data

纵向分类数据多维分析研究

基本信息

批准号：
11680330
负责人：
ADACHI Kohei
金额：
$ 0.83万
依托单位：
Koshien University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

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.

本项目的目的是研究分析纵向分类数据以量化个体变化的方法。我们将重点放在一个指标矩阵上，其行和列分别与时间点上的个人和类别相关联。针对现有量化方法不能对个体变化进行量化的问题，提出了约束正则化量化方法，在约束方法中，对个体在时间点上的得分施加增长曲线约束：将得分约束为时间上的多项式。通过对实际数据的应用，证明了该方法的有效性。在正则化方法中，将已有方法中的损失函数与惩罚函数相结合，形成惩罚损失函数。这种方法细分为两种方法。一种是使用分数的一阶差异来定义处罚，这要求个人分数在时间点上的同质性。另一种是将分数视为时间的自然三次样条函数，并假设每个分数随时间平滑变化，使用样条线的二阶导数来定义惩罚。这两种方法在仿真和实际数据分析中都取得了令人满意的结果。