Application of Random Matrix Theory to social survey data analysis

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K04103
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Sociology
• Research Institution: Ritsumeikan University
• Principal Investigator: Nakai Miki 立命館大学, 産業社会学部, 教授 (00241282)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: ランダム行列理論 / 社会調査データ / 欠損値を含むデータ / カテゴリカル・データ

Outline of Final Research Achievements

During the past three years, the project focused on applying matrix theory methods and computational methods to the optimization of the so-called Missing Data problem. The main results are:
1) The development of a new algorithm to improve and optimize the listwise deletion method. The work is based on identifying what respondents and variables should be deleted to obtain a fully complete dataset without missing data. The optimization technique is semi-analytical and detects the minimum number of deleted respondents and variables. The algorithm has been implemented on the popular computational platform Matlab/Octave.
2) It is important to consider the relative importance of different variables in the analysis before applying complete case analysis. We generalized the algorithm above to include weight factors that quantify what variables cannot be absolutely deleted. The result is a second algorithm that is based on stochastic Monte Carlo optimization. It has been developed in R language.

Free Research Field

社会学

Academic Significance and Societal Importance of the Research Achievements

近年の調査データの統計解析技法の顕著な発展に比して、欠損・欠測を含む社会調査データへの対処手法はあまり注意が払われてこなかったが、その点を考慮しないままだと分析結果は誤ったものになる可能性がある。本研究の成果はそうした起こりうる推定バイアスを回避するための技法上の洗練という点で重要な学術的意義を持つ。また、学際的・国際的な共同研究を進め議論を深めることを通じて、日本のジェンダー不平等や家族にかんするインプリケーションを再考しながら世帯状況を明らかにしたことは社会的意義である。