We study an EM algorithm for estimating product-term regression models with missing data. The study of such problems in the likelihood tradition has thus far been restricted to an EM algorithm method using full numerical integration. However, under most missing data patterns, we show that this problem can be solved analytically, and numerical approximations are only needed under specific conditions. Thus we propose a hybrid EM algorithm, which uses analytic solutions when available and approximate solutions only when needed. The theoretical framework of our algorithm is described herein, along with two numerical experiments using both simulated and real data. We show that our algorithm confers higher accuracy to the estimation process, relative to the existing full numerical integration method. We conclude with a discussion of applications, extensions, and topics of further research.
翻译:我们研究一种EM算法,用缺失的数据来估计产品-周期回归模型。对于这种可能性传统中的问题的研究,到目前为止只限于使用完全数字集成的EM算法。然而,在大多数缺失的数据模式下,我们表明,这个问题可以分析解决,数字近似只在特定条件下才需要。因此,我们建议一种混合的EM算法,在有可用的情况下使用分析性解决办法,仅在需要时使用近似解决办法。这里描述了我们的算法的理论框架,以及使用模拟和真实数据的两次数字实验。我们表明,我们的算法使估算过程比现有的完全数字集成法更加精确。我们最后讨论应用、扩展和进一步研究的专题。