Development of Generalized Odds Ratio Decomposition Method for Socio-Economic Interaction Data

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In this study, the Unbaised Decomposition Method for linearized gravity models, which can be applicable to both cases where diagonal data of socio-economic interaction data matrices an be utilized and where they cannot be utilized, in order to understand statistical properties of the Odds Ratio Decomposition method.1.By examining problems and shortcomings of the Odds Ratio Decomposition method, the importance of the development of a method for linearized gravity models with independent and identical normal distribution errors as the Generalized Odds Ratio Decomposition method is clearly stated.2.The Unbiased Decomposition method is developed and improved using various cross-products rations. Relation, Push, Pull factors and overall adjustment term can be simultaneously estimated by this method.3.Multidimensional Scaling technique is incorporated (Linear-ORDEC-MDS) and more efficient estimates of relation factor can be obtained by this method as coordinated of the latent interaction space. It is also demonstrated that self-relationship which has been fixed and identical is now estimable by this method.4.To handle heteroskedasticity, the Compound Distribution model of inter-regional migration is developed. With this model, the relationship between expected value and variance of migration is clearly shown.5.Linear-ORDEC-ERROR is developed to decompose error terms by combining 6 iteractions among 3 different agents. Probability distribution parameters of interactions is now independently estimable by this method.6.Linear-ORDEC-ND is developed to separately decompose the relation, push and pull factors by combining 4 interactions among 4 different agents to deal with cases where diagonal elements of interaction OD matrices are not available or usable.7.Probability distribution parameters of inter^prefectural migration 1954-2003 are estimated, and it is found out that models without covariances are better fitted than those with covariances.