2000 Fiscal Year Final Research Report Summary
Studies on Multidimensional Analysis of Longitudinal Categorical Data
| Project/Area Number |
11680330
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Koshien University |
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Principal Investigator |
ADACHI Kohei Koshien University, Department of Psychology, Associate Professor., 人間文化学部, 助教授 (60299055)
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| Project Period (FY) |
1999 – 2000
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| Keywords | multivariate analysis / optimal scoring / correspondence analysis / longitudinal data / categorical data / growth curves / regularization / splines |
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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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