Liu Chen-Wei
National Taiwan Normal University, Taipei, Taiwan.
Appl Psychol Meas. 2021 May;45(3):159-177. doi: 10.1177/0146621621990753. Epub 2021 Feb 4.
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.
针对不可忽视的缺失响应的非随机缺失（MNAR）建模通常假定潜在变量分布为二元正态分布。这样的假定很少得到验证，且在实践中常被用作标准。最近针对“完整”项目响应（即无缺失数据）的研究表明，忽略单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结论。然而，目前尚未研究如何处理具有MNAR数据的二元非正态潜在变量分布。本文提议扩展单维经验直方图和大卫曲线方法，以同时处理非正态潜在变量分布和MNAR数据。开展了一项模拟研究来证明忽略二元非正态分布对参数估计的影响，随后对“不知道”项目响应进行了实证分析。本文给出的结果表明，对于MNAR数据，应将检验二元非正态潜在变量分布的假定作为一项常规操作，以尽量减少非正态性对参数估计的影响。
