Evaluation of Multi-parameter Test Statistics for Multiple Imputation

In Ordinary Least Square regression, researchers often are interested in knowing whether a set of parameters is different from zero. With complete data, this could be achieved using the gain in prediction test, hierarchical multiple regression, or an omnibus <i>F</i> test. However, in substantive research scenarios, missing data often exist. In the context of multiple imputation, one of the current state-of-art missing data strategies, there are several different analogous multi-parameter tests of the joint significance of a set of parameters, and these multi-parameter test statistics can be referenced to various distributions to make statistical inferences. However, little is known about the performance of these tests, and virtually no research study has compared the Type 1 error rates and statistical power of these tests in scenarios that are typical of behavioral science data (e.g., small to moderate samples, etc.). This paper uses Monte Carlo simulation techniques to examine the performance of these multi-parameter test statistics for multiple imputation under a variety of realistic conditions. We provide a number of practical recommendations for substantive researchers based on the simulation results, and illustrate the calculation of these test statistics with an empirical example.

在普通最小二乘回归（Ordinary Least Square Regression）中，研究者通常希望验证一组参数是否显著异于零。当数据完整时，可通过预测增益检验、分层多元回归或整体F检验（omnibus F test）达成该目标。然而在实际研究场景中，缺失数据往往难以避免。多重插补（Multiple Imputation）是当前主流的缺失数据处理策略之一，在此框架下已衍生出多种针对一组参数联合显著性的多参数检验方法，这些多参数检验统计量可依托不同分布开展统计推断。但目前学界对这些检验方法的性能了解甚少，且几乎未有研究针对行为科学数据的典型场景（如中小样本量等）对比各类检验的一类错误率与统计功效。本文采用蒙特卡洛模拟（Monte Carlo simulation）技术，在多种贴合实际的研究条件下，检验上述多重插补框架下的多参数检验统计量的性能。基于模拟结果，本文为实际研究者提供了若干实用建议，并通过一则实证案例演示了这些检验统计量的计算流程。