Schulz Susanne, Zondervan-Zwijnenburg Mariëlle, Nelemans Stefanie A, Veen Duco, Oldehinkel Albertine J, Branje Susan, Meeus Wim
Youth and Family, Utrecht University, Utrecht, Netherlands.
Methodology and Statistics, Utrecht University, Utrecht, Netherlands.
Front Psychol. 2021 Mar 24;12:620802. doi: 10.3389/fpsyg.2021.620802. eCollection 2021.
Bayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.
The sample consisted of 102 mother-adolescent dyads (39.2% girls, T1 = 13.0). Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the (power) priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.
The prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.
A systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations (e.g., the prior is an updated Bayesian distribution), and may also be affected by pragmatic considerations regarding the impact of the previous results at hand (e.g., extremely specific previous results).
带有信息性先验的贝叶斯估计允许用新数据更新先前的研究结果，从而积累知识。为了减少该过程中的主观性，本研究强调如何系统地权衡和指定信息性先验，并通过一个实证例子突出了不同汇总方法的使用。该实证例子采用三年纵向多方法设计，考察了观察到的母亲 - 青少年积极和消极互动行为是否介导了从青春期早期到中期母亲与青少年内化症状之间的关联。
样本包括102对母亲 - 青少年二元组（女孩占39.2%，T1 = 13.0岁）。母亲和青少年报告了他们的内化症状，并在冲突任务中观察他们的互动行为。我们系统地搜索了先前的研究，并使用专家提供的加权系统来考虑其相关性。随后，我们使用三种方法汇总（功效）先验：线性合并、对数合并以及通过最大似然估计将正态分布拟合到线性合并结果上。我们比较了三种不同指定的信息性先验和默认先验对先验预测分布、收缩以及后验估计的影响。
三种信息性先验的先验预测分布非常相似，且以观察到的数据均值为中心。收缩结果表明，对数合并先验受数据影响最小。大多数后验估计在不同先验之间相似。一些先前的研究包含极其具体的信息，导致在线性合并先验分布的分析中出现双峰后验分布。拟合正态先验和默认先验之后的后验非常相似。总体而言，我们发现母亲而非青少年的内化症状预测了随后的母亲 - 青少年互动行为，而消极互动行为似乎预测了随后的内化症状。关于中介效应的证据仍然有限。
对先前信息的系统搜索和专家构建的加权系统有助于明确指定功效先验。先前多项研究的信息应如何纳入先验取决于理论考量（例如，先验是更新后的贝叶斯分布），也可能受到关于手头先前结果影响的实际考量（例如，极其具体的先前结果）的影响。
