Test for symmetry in $2\times 2$ contingency tables with nonignorable nonresponses

The McNemar test evaluates the hypothesis that two correlated proportion is common in $2\times 2$ contingency tables with the same categories. This study discusses a test for symmetry in $2\times 2$ contingency tables with nonignorable nonresponses. The proposed method is based on Takai and Kano (2008), which discusses a test for independence because a dependency assumption between the two observed outcomes is required to obtain an identification. Here, we focus on three models and propose a test for symmetry in $2\times 2$ contingency tables with nonignorable nonresponses.