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Bias Introduced by Rounding in Multiple Imputation for Ordered Categorical Variables

机译：有序分类变量的多重插补中舍入引入的偏差

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摘要

Multivariate normality is frequently assumed when multiple imputation is applied for missing data. When data are ordered categorical, imputing missing data using the fully normal imputation results in implausible values falling outside of the categorical values. Naive rounding has been suggested to round the imputed values to their categorical neighbors for further analysis. Previous studies showed that, for binary data, the rounded values can result in biased mean estimation when the population distribution is asymmetric. However, it has been conjectured that as the number of categories increases, the bias will decrease. To investigate this conjecture, the present study derives the formulas for the biases of the mean and standard deviation for ordered categorical variables with naive rounding. Results show that both the biases of the mean and standard deviation decrease as the number of categories increases from 3 to 9. This study also finds that although symmetric population distributions lead to unbiased means of the rounded Values, the standard deviations may still be largely biased. A simulation studyfurther shows that the biases due to naive rounding can result in substantially low coverage rates for the population mean parameter.
机译：对丢失的数据进行多次插补时，经常采用多元正态性。对数据进行分类排序时，使用完全正常的插补来插补丢失的数据会导致难以置信的值落在分类值之外。已建议采用朴素的舍入将估算的值舍入到其分类的邻居，以进行进一步分析。先前的研究表明，对于二元数据，当总体分布不对称时，四舍五入的值可能会导致均值估计偏差。但是，可以推测，随着类别数量的增加，偏差将减小。为了研究这个猜想，本研究得出了带有天真舍入的有序分类变量均值和标准差的偏差的公式。结果表明，随着类别数从3增加到9，均值偏差和标准偏差均减小。该研究还发现，尽管总体分布对称导致四舍五入值的均值不变，但标准偏差仍可能存在较大偏差。 。进一步的模拟研究表明，由于天真舍入而产生的偏差可能导致总体均值参数的覆盖率大大降低。

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