Can a linear combination model be scientific explanation? Integration of mathematical sociology and empirical social research in class identification study

A linear combination model of explanatory variables such as a multiple regression analysis is often used as the simplest approximation of true relation between explanatory and response variable. This paper shows that a linear combination model can be logically derived from the models of mathematical sociology that consist of sociological assumptions and attempts to give a linear combination model theoretical ground. We show that a linear combination model can be an explanatory model rather than just a curve-fitting model. In the context of studies of class identification, we show that the Farao-Kosaka model and the inherited status model can be a theoretical ground for a linear combination model of class identification and clarify the condition that is needed for an integrated development of mathematical sociology and sociometrics in the field of social stratification.