Cremers Jolien, Mulder Kees Tim, Klugkist Irene
Department of Methodology and Statistics, Utrecht University, The Netherlands.
Research Methodology, Measurement and Data Analysis, Behavioural Sciences, University of Twente, Enschede, The Netherlands.
Br J Math Stat Psychol. 2018 Feb;71(1):75-95. doi: 10.1111/bmsp.12108. Epub 2017 Sep 4.
The interpretation of the effect of predictors in projected normal regression models is not straight-forward. The main aim of this paper is to make this interpretation easier such that these models can be employed more readily by social scientific researchers. We introduce three new measures: the slope at the inflection point (b ), average slope (AS) and slope at mean (SAM) that help us assess the marginal effect of a predictor in a Bayesian projected normal regression model. The SAM or AS are preferably used in situations where the data for a specific predictor do not lie close to the inflection point of a circular regression curve. In this case b is an unstable and extrapolated effect. In addition, we outline how the projected normal regression model allows us to distinguish between an effect on the mean and spread of a circular outcome variable. We call these types of effects location and accuracy effects, respectively. The performance of the three new measures and of the methods to distinguish between location and accuracy effects is investigated in a simulation study. We conclude that the new measures and methods to distinguish between accuracy and location effects work well in situations with a clear location effect. In situations where the location effect is not clearly distinguishable from an accuracy effect not all measures work equally well and we recommend the use of the SAM.
预测变量在投影正态回归模型中的效应解释并非直截了当。本文的主要目的是使这种解释更简便，以便社会科学研究人员能更轻松地运用这些模型。我们引入了三种新的度量：拐点处的斜率（b）、平均斜率（AS）和均值处的斜率（SAM），它们有助于我们评估贝叶斯投影正态回归模型中预测变量的边际效应。当特定预测变量的数据不靠近圆形回归曲线的拐点时，最好使用SAM或AS。在这种情况下，b是一种不稳定的外推效应。此外，我们概述了投影正态回归模型如何使我们能够区分对圆形结果变量均值和离散程度的效应。我们分别将这些类型的效应称为位置效应和精度效应。在一项模拟研究中，我们考察了这三种新度量以及区分位置效应和精度效应的方法的性能。我们得出结论，在具有明显位置效应的情况下，区分精度效应和位置效应的新度量和方法效果良好。在位置效应与精度效应难以明确区分的情况下，并非所有度量的效果都同样好，我们建议使用SAM。
