A fundamental aspect of statistics is the integration of data from different sources. Classically, Fisher and others were focused on how to integrate homogeneous (or only mildly heterogeneous) sets of data. More recently, as data is becoming more accessible, the question of if data sets from different sources should be integrated is becoming more relevant. The current literature treats this as a question with only two answers: integrate or don't. Here we take a different approach, motivated by information-sharing principles coming from the shrinkage estimation literature. In particular, we deviate from the do/don't perspective and propose a dial parameter that controls the extent to which two data sources are integrated. How far this dial parameter should be turned is shown to depend, for example, on the informativeness of the different data sources as measured by Fisher information. In the context of generalized linear models, this more nuanced data integration framework leads to relatively simple parameter estimates and valid tests/confidence intervals. Moreover, we demonstrate both theoretically and empirically that setting the dial parameter according to our recommendation leads to more efficient estimation compared to other binary data integration schemes.

翻译：统计学的一个基本方面是整合来自不同来源的数据。经典地，费希尔等人专注于如何整合同质性（或仅轻微异质性）的数据集。近期，随着数据日益可得，不同来源的数据集是否应当整合的问题变得愈加重要。现有文献将此视为一个仅有两种答案的问题：整合或不整合。本文采取了不同的方法，其动机源于收缩估计文献中的信息共享原理。具体地，我们摒弃了整合/不整合的二分视角，提出一个控制数据源整合程度的旋钮参数。研究表明，这一旋钮参数应被调整的程度取决于不同数据源的信息量（例如，以费希尔信息衡量）。在广义线性模型的背景下，这一更精细的数据整合框架可导出相对简单的参数估计及有效的检验/置信区间。此外，我们从理论和实证两方面证明，与二值数据整合方案相比，依据我们的建议设定旋钮参数能实现更高效的估计。