正态插补模型是否应修改为插补偏态变量？
Should a Normal Imputation Model Be Modified to Impute Skewed Variables?
摘要：
研究人员经常在正态性假设下估算连续变量，但许多不完全变量是偏斜的。我们发现，在正态模型下输入偏斜的连续变量会导致偏倚;对于常用的被估量（如均值、标准差和线性回归系数），偏倚通常是轻微的，但对于更多的形状依赖被估量（如偏度或偏度系数），偏倚可能是严重的。我们测试了几种适应正态插补模型以适应偏度的方法，包括转换、截断或删失（舍入）正常插补值的方法，以及从二次或截尾回归中插补值的方法。这些修改都不能可靠地降低正态模型的偏差，有些修改会使偏差变得更糟。我们的结论是，如果必须在正态模型下估算一个偏斜变量，通常最安全的方法是不进行修改-除非你对估计平均值，方差和回归的估计更感兴趣。在结论中，我们简要地讨论了有前途的发展领域的连续插补模型，不假设正态。
英文摘要：
Researchers often impute continuous variables under an assumption of normality, yet many incomplete variables are skewed. We find that imputing skewed continuous variables under a normal model can lead to bias; the bias is usually mild for popular estimands such as means, standard deviations, and linear regression coefficients, but the bias can be severe for more shape-dependent estimands such as percentiles or the coefficient of skewness. We test several methods for adapting a normal imputation model to accommodate skewness, including methods that transform, truncate, or censor (round) normally imputed values, as well as methods that impute values from a quadratic or truncated regression. None of these modifications reliably reduces the biases of the normal model, and some modifications can make the biases much worse. We conclude that, if one has to impute a skewed variable under a normal model, it is usually safest to do so without modifications -- unless you are more interested in estimating percentiles and shape that in estimated means, variance, and regressions. In the conclusion, we briefly discuss promising developments in the area of continuous imputation models that do not assume normality.
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