Applying mathematical modelling to the factor analyses of obtaining GASR funds for universities in Japan

First, we briefly explain the historical trend of the Japanese competitive research funding system, focusing on the grants-in-aid for scientific research (GASR). We provide mathematical models, such as logistic curves and Zipf's model, to explain the trend of budgets for research promotion funds and their allocation to Japanese universities and research institutions. Subsequently, we evaluate the performance of Japanese universities from the perspective of obtaining GASR funds using Gini coefficients. We then build multiple regression models to quantitatively investigate the factors that determine and affect the dependent variables, such as the number of accepted GASR projects and number of distributed funds of the GASF projects, in which independent variables including the number of undergraduate students, external funds, operating expenses grants, and operating expenses grants to all university-specific project expenses, or the ratio of external funds per faculty member, may also be considered as influential factors. We apply multivariate analysis techniques such as cluster analysis and principal component analysis to determine the key factors for obtaining GASR, to classify Japanese universities with respect to their recent scenario for obtaining GASR funds and reveal the determining factors underlying these results.