Understanding many-to-many matching relationship and its correlation with joint response

Many-to-many matching relationship in a two-sided market has been widely observed in today's transportation activities. Observation of such matching relationship raises some interesting questions: what factors drive the matching of two agents? Is the formation of matching relationship related with joint behavior which may lead to different understandings of planning and operation? To answer these questions, econometric models may be the best methodology. However, to the authors' best knowledge, there lacks a well-established econometric model to explain the observed data that contains matching relationship in a two-sided transportation market. Therefore, this paper proposes an innovative ordinal joint response model to bridge the gap. The proposed model consists of two regression equations: the first uses a latent dependent variable to disentangle the many-to-many matching relationship; the second specifies an ordered probit equation to investigate the ordinal outcome of joint behavior. Error terms of the two equations are assumed correlated to capture the correlation of the matching process and joint behavior. An example of airline-airport matching is used to demonstrate the proposed model.