在本文中，我們為二元縱向計數資料建立聯合模型，此類資料只能在特定時間點上被蒐集。在模型的架構中，我們假設每一種事件類型的計數服從一個非齊次Poisson過程，並使用比例均值迴歸模型建構事件發生率。為了將二元資料內的關聯性納入模型，我們考慮在每一個事件類型的均值函數內存在隨機效應，而提出的模型允許此二元縱向計數資料可以透過包含於均值函數內的隨機效應使其建立相依性，這些隨機效應服從一個邊際分佈為Gamma分佈的Sarmanov分佈。在此隨機模型假設下，我們推導出二元縱向計數資料的聯合機率分佈，並利用最大概似估計法取得參數估計。我們使用模擬比較兩種估計方法下所得之估計量的表現，從模擬的結果中可以觀察到兩者的表現相似。最後，本文所提出之模型套用在內政部警政署的交通資料，估計協變量與季節對於車禍發生率的影響。

In this work, we consider a joint model for panel count data with bivariate event types, which are only collected at particular time points. We assume that the counts follow a nonhomogeneous Poisson process for each event type, and a proportional mean regression model is specified. To account for the association, we further impose a positive random effect on each of the mean functions. The proposed model allows for the dependence of event types through random effects that follow the bivariate Sarmanov distribution with gamma marginals. The estimations of the parameters are based on the maximum likelihood method. We use two estimation methods and compare the performance of the estimators based on several simulation studies, which result in similar performance. An application to traffic accident data is presented.

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