Department of Psychology, University of California, Davis, CA 95616, USA.
Psychol Methods. 2012 Dec;17(4):615-22. doi: 10.1037/a0030003. Epub 2012 Sep 17.
Re-parameterized regression models may enable tests of crucial theoretical predictions involving interactive effects of predictors that cannot be tested directly using standard approaches. First, we present a re-parameterized regression model for the Linear × Linear interaction of 2 quantitative predictors that yields point and interval estimates of 1 key parameter-the crossover point of predicted values-and leaves certain other parameters unchanged. We explain how resulting parameter estimates provide direct evidence for distinguishing ordinal from disordinal interactions. We generalize the re-parameterized model to Linear × Qualitative interactions, where the qualitative variable may have 2 or 3 categories, and then describe how to modify the re-parameterized model to test moderating effects. To illustrate our new approach, we fit alternate models to social skills data on 438 participants in the National Institute of Child Health and Human Development Study of Early Child Care. The re-parameterized regression model had point and interval estimates of the crossover point that fell near the mean on the continuous environment measure. The disordinal form of the interaction supported 1 theoretical model-differential-susceptibility-over a competing model that predicted an ordinal interaction.
重新参数化的回归模型可以检验涉及预测变量交互作用的关键理论预测，而这些交互作用不能通过标准方法直接检验。首先，我们提出了一个用于 2 个定量预测变量的线性 × 线性交互作用的重新参数化回归模型，该模型产生了 1 个关键参数（预测值的交叉点）的点估计和区间估计，同时保持其他某些参数不变。我们解释了如何使用产生的参数估计来提供区分有序和无序交互作用的直接证据。我们将重新参数化的模型推广到线性 × 定性交互作用，其中定性变量可能有 2 个或 3 个类别，然后描述如何修改重新参数化的模型来检验调节效应。为了说明我们的新方法，我们对 438 名参加国家儿童健康与人类发展研究所早期儿童保育研究的参与者的社会技能数据拟合了替代模型。重新参数化的回归模型对交叉点的点估计和区间估计接近连续环境测量的平均值。交互作用的无序形式支持了 1 个理论模型——差异性易感性——而不是预测有序交互作用的竞争模型。
