Lee Sunbok, Lei Man-Kit, Brody Gene H
Center for Family Research, University of Georgia.
Psychol Methods. 2015 Jun;20(2):245-58. doi: 10.1037/met0000033. Epub 2015 Apr 6.
Distinguishing between ordinal and disordinal interaction in multiple regression is useful in testing many interesting theoretical hypotheses. Because the distinction is made based on the location of a crossover point of 2 simple regression lines, confidence intervals of the crossover point can be used to distinguish ordinal and disordinal interactions. This study examined 2 factors that need to be considered in constructing confidence intervals of the crossover point: (a) the assumption about the sampling distribution of the crossover point, and (b) the possibility of abnormally wide confidence intervals for the crossover point. A Monte Carlo simulation study was conducted to compare 6 different methods for constructing confidence intervals of the crossover point in terms of the coverage rate, the proportion of true values that fall to the left or right of the confidence intervals, and the average width of the confidence intervals. The methods include the reparameterization, delta, Fieller, basic bootstrap, percentile bootstrap, and bias-corrected accelerated bootstrap methods. The results of our Monte Carlo simulation study suggest that statistical inference using confidence intervals to distinguish ordinal and disordinal interaction requires sample sizes more than 500 to be able to provide sufficiently narrow confidence intervals to identify the location of the crossover point.
在多元回归中区分有序交互作用和无序交互作用，对于检验许多有趣的理论假设很有用。由于这种区分是基于两条简单回归线交叉点的位置做出的，所以交叉点的置信区间可用于区分有序和无序交互作用。本研究考察了在构建交叉点置信区间时需要考虑的两个因素：(a) 关于交叉点抽样分布的假设，以及 (b) 交叉点置信区间异常宽的可能性。进行了一项蒙特卡罗模拟研究，以比较构建交叉点置信区间的6种不同方法在覆盖率、真值落在置信区间左侧或右侧的比例以及置信区间的平均宽度方面的情况。这些方法包括重新参数化、德尔塔、菲勒、基本自助法、百分位数自助法和偏差校正加速自助法。我们的蒙特卡罗模拟研究结果表明，使用置信区间来区分有序和无序交互作用的统计推断需要样本量超过500，以便能够提供足够窄的置信区间来确定交叉点的位置。
