在生醫或其他領域中，常會面臨配對二元次數資料（paired bivariate count data） 之分析問題。例如，病患分別於A、B醫院之診斷結果或就診次數皆為具相關性 的資料，而後者或許呈現負相關。 為了描述負相關結構個數資料，Famoye (2010) 提出了雙變量負二項模型， 透過崁入相關性結構於二個單變量負二項模型中，並加入調控相關係數參數，使 模型可處理正、負相關問題。然而，該崁入項也讓模型結構相對複雜，並增加參 數估計的條件限制與影響統計推論上的正確性。本研究將顯示Famoye (2010) 提 出之雙變量負二項模型在建模上、推論上的缺點。同時，我們將藉由模擬及實例 分析展示強韌化 (Royall與Tsou，2003) 後的二元負二項概似函數分析正、負相 關資料之表現優於Famoye (2010) 提出之雙變量負二項模型。;In biomedical and related fields， paired bivariate count data are commonly encountered， where dependence between two count variables naturally arises. For instance， the number of medical visits or diagnostic outcomes for the same patient recorded at different hospitals may exhibit substantial dependence， including negative correlation. To accommodate such dependence structures， Famoye (2010) proposed a bivariate negative binomial model that incorporates a multiplicative adjustment term linking two marginal negative binomial distributions. This construction introduces a dependence parameter that enables the model to capture both positive and negative correlations. Despite its flexibility， the resulting model becomes structurally complex， imposes restrictive conditions on parameter estimation， and may compromise the reliability of statistical inference. To address these issues， we suggest the robust likelihood framework proposed by Royall and Tsou (2003) and develop a robust bivariate negative binomial likelihood. Our results show that robust method is more stable and reliable inference for both positively and negatively dependent count data.
