Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates are not the result of data analysis and may therefore be termed 'analytic composites'. However, it has already been shown that the variance contributions of indicators within analytic composites are affected by the indicator variance and indicator inter-correlations. In the present study purely analytic composites are proposed, having exactly the variance contribution of indicators within the composites that are a priori defined by the indicator weights. An example based on simulated data illustrates the difference between analytic composites and purely analytic composites. As an application area, we propose that purely analytic composites could be of interest in the exchange-traded fund. An R-script for the computation of purely analytic composites is given in the Appendix.

翻译：复合指标常被构建以辅助决策者工作。因此，实践或理论考量可能导致构成复合指标的指标具有先验权重。通过加权聚合创建的复合指标并非数据分析的结果，因此可称为"分析型复合指标"。然而已有研究表明，在分析型复合指标中，指标的方差贡献受到指标自身方差及指标间相关性的影响。本研究提出纯粹分析型复合指标，其指标在复合指标中的方差贡献恰好与先验权重定义的指标权重完全一致。基于模拟数据的算例说明了分析型复合指标与纯粹分析型复合指标的差异。我们提出，纯粹分析型复合指标在交易所交易基金领域具有潜在应用价值。附录提供了用于计算纯粹分析型复合指标的R语言脚本。