Introduction and Demonstration of the Many-Group Matching (MAGMA)-Algorithm: Matching Solutions for Two or More Groups

Field data is often limited regarding causal inference. This is partly because randomization techniques are often impractical or unethical within certain fields (e.g., randomly assigning individuals to different types of classroom instruction in educational settings). Matching procedures, like propensity score matching (PSM; Rosenbaum & Rubin, 1983), are regularly used to strengthen interpretations of group membership-effects in field research. By matching individuals from different subgroups of a field sample (e.g., participations vs. nonparticipation in a special education program), relevant confounds to group membership-effects (e.g., socio-economic status) can be balanced out and thereby eliminated retrospectively. That way, matching turns field data into quasi-experimental data. Currently, the most prominent approach to matching individuals is nearest neighbor matching (NNM) (see Austin, 2014; Austin & Stuart, 2015; Heinz et al., 2022; Jacovidis, 2017).
Available statistical software (e.g., R-packages like MatchIt, Ho et al., 2011), however, does not fully realize the potential of NNM to reduce sample-related bias in field data due to unsystematic procedures for the identification of apt pairs to match. Furthermore, existing matching applications are limited to two-group designs (that being said, weighting applications for more than two groups do exists, e.g., MMW-S, Hong, 2012). In addition, balance estimation, as a matching quality check, is often conducted rudimentarily (e.g., by solely reporting between-group post-matching differences). So far, conventions on balance estimation for more than two groups are absent.
To address these shortcomings, we developed a systematic algorithm, designed for matching individuals from two or more groups alongside a set of adequate balance estimates. We call it “MAGMA” (for MAny-Group MAtching). In this work, we demonstrate and evaluate the MAGMA-algorithm, using two empirical examples from extensive field data.

领域数据在因果推断方面往往受限。这部分原因在于，在某些领域（例如，在教育环境中随机分配个体至不同类型的课堂指导）中，随机化技术往往不切实际或存在道德伦理问题。匹配程序，如倾向得分匹配（PSM；Rosenbaum & Rubin, 1983），在田野研究中常被用于强化对群体成员效应的解释。通过匹配来自田野样本不同子群体（例如，特殊教育项目的参与与非参与）的个体，可以平衡并最终消除与群体成员效应相关的混杂因素（例如，社会经济地位）。从而，匹配将田野数据转化为准实验数据。目前，最显著的匹配个体方法为最近邻匹配（NNM）（参见 Austin, 2014；Austin & Stuart, 2015；Heinz et al., 2022；Jacovidis, 2017）。然而，现有的统计软件（例如，R 包 MatchIt，Ho et al., 2011）并未充分实现NNM在减少田野数据样本相关偏差方面的潜力，这是由于在识别匹配配对时的非系统性程序。此外，现有的匹配应用局限于两组设计（尽管存在超过两组的加权应用，例如，MMW-S，Hong, 2012）。此外，作为匹配质量检查的平衡估计通常被粗略地进行（例如，仅通过报告匹配后组间差异）。迄今为止，对于超过两组的平衡估计尚无约定。为了解决这些不足，我们开发了一种系统算法，旨在匹配来自两组或更多组的人员，并配备一系列充分的平衡估计。我们称之为“MAGMA”（代表多组匹配）。在本研究中，我们展示了MAGMA算法，并使用广泛的田野数据中的两个实证示例对其进行了评估。