Missing not at random (MNAR) modeling for non-ignorable missing responses usually assumes that the latent variable distribution is a bivariate normal distribution. Such an assumption is rarely verified and often employed as a standard in practice. Recent studies for “complete” item responses (i.e., no missing data) have shown that ignoring the nonnormal distribution of a unidimensional latent variable, especially skewed or bimodal, can yield biased estimates and misleading conclusion. However, dealing with the bivariate nonnormal latent variable distribution with present MNAR data has not been looked into. This article proposes to extend unidimensional empirical histogram and Davidian curve methods to simultaneously deal with nonnormal latent variable distribution and MNAR data. A simulation study is carried out to demonstrate the consequence of ignoring bivariate nonnormal distribution on parameter estimates, followed by an empirical analysis of “don’t know” item responses. The results presented in this article show that examining the assumption of bivariate nonnormal latent variable distribution should be considered as a routine for MNAR data to minimize the impact of nonnormality on parameter estimates.

针对不可忽略的缺失响应的非随机缺失 (MNAR) 建模通常假设潜在变量分布是二元正态分布。这种假设很少得到验证，并且在实践中经常被用作标准。最近对“完整”项目响应（即无缺失数据）的研究表明，忽略一维潜在变量的非正态分布，尤其是偏态或双峰分布，可能会产生有偏差的估计和误导性的结论。然而，尚未研究使用现有 MNAR 数据处理双变量非正态潜变量分布。本文提出扩展一维经验直方图和戴维曲线方法来同时处理非正态潜变量分布和 MNAR 数据。进行模拟研究以证明忽略参数估计的二元非正态分布的后果，然后对“不知道”项目响应进行实证分析。本文提出的结果表明，检查二元非正态潜变量分布的假设应被视为 MNAR 数据的常规操作，以尽量减少非正态性对参数估计的影响。