Supplementary Material for: The association between education and cognitive performance varies at different levels of cognitive performance: a quantile regression approach

Introduction
Educational differences in cognitive performance among older adults are well-documented. Studies that explore this association typically estimate a single average effect of education on cognitive performance. We argue that the processes that contribute to the association between education and cognitive performance are unlikely to have equal effects at all levels of cognitive performance. In this study, we employ an analytical approach that enables us to go beyond averages to examine the association between education and five measures of global and domain-specific cognitive performance across the outcome distributions.

Methods
This cross-sectional study included 1780 older adults aged 58–68 years from the Longitudinal Aging Study Amsterdam (LASA). Conditional quantile regression was used to examine variation across the outcome distribution. Cognitive outcomes included Mini-Mental State Examination score (MMSE), crystallized intelligence, information processing speed, episodic memory, and a composite score of global cognitive performance.

Results
The results showed that the associations between education and different cognitive measures varied across the outcome distributions. Specifically, we found that education had a stronger association with crystallized intelligence, MMSE, and a composite cognitive performance measure in the lower tail of the performance distributions. The associations between education and information processing speed and episodic memory were uniform across the outcome distributions.

Conclusion
Larger associations between education and some domains of cognitive performance in the lower tail of the performance distributions implies that inequalities are primarily generated among individuals with lower performance, rather than among average and high performers. Additionally, the varying associations across some of the outcome distributions indicate that estimating a single average effect through standard regression methods may overlook variations in cognitive performance between educational groups. Future studies should consider heterogeneity across the outcome distribution.

引言
老年人群认知表现的教育差异已有充分研究证实。现有探索该关联的研究通常仅估算教育对认知表现的单一平均效应。我们认为，驱动教育与认知表现间关联的各类过程，在认知表现的不同水平上未必产生等同的影响。本研究采用一种分析方法，得以突破平均效应的局限，在结果分布维度下考察教育与五项全局及领域特异性认知表现指标间的关联。
方法
本横断面研究纳入了来自阿姆斯特丹纵向衰老研究（Longitudinal Aging Study Amsterdam, LASA）的1780名年龄介于58至68岁的老年人。研究采用条件分位数回归（Conditional quantile regression）方法，考察结果分布中的变异情况。认知结局指标包括简易精神状态检查（Mini-Mental State Examination, MMSE）得分、晶体智力（crystallized intelligence）、信息加工速度（information processing speed）、情景记忆（episodic memory）以及全局认知表现综合得分。
结果
研究结果显示，教育与不同认知指标间的关联随结果分布呈现异质性。具体而言，在认知表现分布的下尾部，教育与晶体智力、简易精神状态检查得分及全局认知表现综合得分的关联更强。而教育与信息加工速度、情景记忆间的关联在各结果分布中均保持一致。
结论
在认知表现分布的下尾部，教育与部分认知领域的关联更强，这意味着认知表现的不平等主要产生于低认知表现人群，而非中等及高认知表现人群。此外，部分认知领域的关联随结果分布呈现异质性，提示通过标准回归方法估算单一平均效应可能会忽视不同教育组人群间的认知表现差异。未来研究应考虑结果分布维度下的异质性。