关键词: 社区发现算法, 代际流动表, 对数线性模型, 矩阵谱分析

Abstract: The frequency of interaction between the data of the intergenerational flow table and the data of the parent’s social status reflects the superiority and inferiority of social resources in the comparison between the parent and son. The empirical investigation of the evolution of the basic social characteristics of wealth, class, privilege, etc. depends on the quantitative analysis of the intergenerational flow table. Log-linear model is the basic tool for flow table modeling analysis. By fitting the cell frequency of the contingency table, we can identify the strong and weak interactions between the row classification and the column classification of the flow table, then describe the interaction structure of the social status between parent and son. However, in the process of modeling empirical data, it is often encountered that the fitting accuracy of the reduced log-linear model cannot pass the test. Existing linear equation variable selection methods can improve the fitting effect of the model, but there are problems that the modeling results are difficult to match the social mobility theory, and there is no clear guiding significance for the induction and abstract social mobility models. In the social flow table, the social status between the son and the parent constitutes a social network. The paper applies the complex network community discovery algorithm to discover the social association structure between parent and son. Aiming at the problem of insufficient precision of the reduced loglinear model, a new modeling idea is proposed: the community discovery algorithm is used to mine the residual contingency table of the reduced loglinear model, and the discovered community effect is added. Parameter constraint is introduced into the original loglinear model to improve the fitting of the data. Since only one parameter constraint is added to the original reduced loglinear model, the simplicity and theoretical significance of the modeling result can be guaranteed. At the same time, the community effect complements the interpretation of the empirical data structure by the original log-linear model. We use this method to model and analyze the empirical intergenerational occupational flow table derived from China’s comprehensive social survey data, which better explains the association model between the son occupational class and the parent’s occupational class.

Key words: Community Discovery Algorithm, Intergenerational Flow Table, Loglinear Model, Matrix Spectrum Analysis