研究期間：10208~10307;The method of composite likelihood was introduced by Lindsay (1988) for correlated data. This parametric approach provides consistent regression parameter estimates and can be used to create likelihood ratio test. However, some drawbacks are notable. For example, the large sample composite likelihood ratio test doesn't have the familiar standard chi-square distribution, and no legitimate likelihood function is available by the composite likelihood when model assumption fails. The multivariate negative binomial distribution has been shown to be a superb simple working model for analyzing correlated data. One can operate on the robust negative binomial likelihood function to acquire legitimate likelihood-based inferential tools, such as the likelihood ratio and the score tests and goodness of fit test. There are two goals this research proposal wishes to accomplish. One is to establish composite likelihood using the multivariate negative binomial distribution as the core model. Secondly, we will contrast the normal-based composite likelihood and the negative binomial-based composite likelihood in terms of 1) legitimacy 2) efficiency and 3) simplicity, when the score model assumption fails. According to the plentiful experiences on robust likelihood, we are confident that the latter will be a better choice for correlated data under model misspecifications.