Department of Psychology, Philipps University of Marburg.
Psychol Rev. 2021 Nov;128(6):1187-1196. doi: 10.1037/rev0000316.
Davis-Stober and Regenwetter (2019; D&R) showed that even when all predictions of a theory hold in separate studies, not even a single individual may be described by all predictions jointly. To illustrate this "paradox" of converging evidence, D&R derived upper and lower bounds on the proportion of individuals for whom all predictions of a theory hold. These bounds reflect extreme positive and negative stochastic dependence of individual differences across predictions. However, psychological theories often make more specific assumptions such as true individual differences being independent or positively correlated (e.g., due to a common underlying trait). Based on this psychometric perspective, I extend D&R's conceptual framework by developing a multivariate normal model of individual effects. Assuming perfect consistency (i.e., a correlation of one) of individual effects across predictions, the proportion of individuals described by all predictions of a theory is identical to D&R's upper bound. The proportion drops substantially when assuming independence of individual effects. However, irrespective of the assumed correlation structure, the multivariate normal model implies a lower bound that is strictly above D&R's lower bound if a theory makes at least three predictions. Hence, the scope of a theory can be improved by specifying whether individual effects are assumed to show a certain level of consistency across predictions (similar to a trait) or whether they are statistically independent (similar to a state). (PsycInfo Database Record (c) 2021 APA, all rights reserved).
戴维斯-斯托伯和雷根沃特（2019 年；D&R）表明，即使一个理论的所有预测在单独的研究中都成立，也没有一个个体可以被所有预测共同描述。为了说明这种“矛盾”的证据汇聚，D&R 推导出了一个理论的所有预测都成立的个体比例的上限和下限。这些界限反映了个体差异在预测之间的极端正和负随机依赖。然而，心理学理论通常做出更具体的假设，例如真实的个体差异是独立的或正相关的（例如，由于共同的潜在特质）。基于这种心理测量学的观点，我通过开发个体效应的多元正态模型来扩展 D&R 的概念框架。假设个体效应在预测之间具有完美的一致性（即相关系数为一），那么一个理论的所有预测所描述的个体比例与 D&R 的上限相同。当假设个体效应相互独立时，这个比例会大幅下降。然而，无论假设的相关结构如何，多元正态模型都暗示了一个下限，如果一个理论做出至少三个预测，那么这个下限严格高于 D&R 的下限。因此，如果个体效应被假设在预测之间表现出一定程度的一致性（类似于特质）或者它们在统计上是独立的（类似于状态），那么理论的范围可以通过指定来得到改善。（PsycInfo 数据库记录（c）2021 APA，保留所有权利）。
