Simon Out of Homans by Coleman

Simon's linear model for some of Homans's propositions about small groups is imbedded in a more general system of coupled linear differential equations in group averages as variables. It is successfully translated into differential equations about flows of proportions of men among cells in a cross-classification, equations adapted from Coleman's Introduction to Mathematical Sociology. Simon's unmeasurable averages are operationalized as the marginals in the 2 X 2 table and can be found directly from two coupled equations in the marginals, if the rate parameters satisfy certain constraints. An additional independent equation reflects a correlation of attributes across individuals not considered by Simon. Several ways to estimate parameters and test the model are discussed.