从0.5到0.75 不同PRI阈值的参考文献
来自: Ratatouille(Ideas are bulletproof)
最近刚写完篇论文，中途发现PRI阈值0.7太高了，导致出来的组态就只有一个，就花时间找了一下更低一点的PRI阈值，现在论文已经完成了，顺便整理一下PRI阈值的参考文献。
首先，在真值表分析时原始一致性为0.8这个基本没有疑问，其次，很重要的一点是也要结合PRI阈值来筛选组态，否则得出来的组态条件既可能是结果的一个充分条件，它的非集也可能是结果的一个充分条件，即 X → Y，～X → Y，而这显然是不合常理的，也不符合因果推断的基本条件：如果X的存在与否都会导致Y （X存在与缺失不会对Y造成差异），那么X显然不是Y的一个原因，因为原因应该是差异制造者（difference-maker）。
喜欢闷着头执着于软件操作不喜欢理解原理哪怕理解原理并不复杂而在操作软件过程中遇到诸多疑问却帖子论文也不搜就来保姆式提问的学习偷懒的同学下面的话就不用看了。
感兴趣的同学可以在Excel里面做个简单的模拟研究，假设案例为100个，生成7个（依次命名为X1-X7）随机条件变量（用Excel函数生成数值在0-1之间的随机数），一个结果变量，命名为Y。然后生成一个组态也就是X1到X7的交集，用函数min（X1，X2，X3，X4，X5，X6，X7）算出这个解的得分标记为A，然后再算出A的非集，标记为～A。保存好后用fsQCA 打开，利用绘图功能，分别算出A对Y的充分一致性，和～A → Y的充分一致性，不出意外的话，这俩的一致性都很高，说明A可以促成Y，非A也可以促成Y，而这显然是一个矛盾，原因如上。而这俩组态的PRI一致性应该出奇地低，这个可以用R 中的”QCA“做充分性分析看出来。
或者生成7个随机条件变量和1个结果变量后，用fsQCA打开，然后用原始一致性0.8筛选组态，进而生成结果，会发现随机生成的变量间的组合竟然也构成结果的一个充分条件，而这显然也是不对的，因为既然所有变量都是随机的，应该变量间不存在稳定的一致性联系，无论条件怎么组合，他们也不可能跟结果产生任何有意义的关系，更不可能构成结果的一个充分条件。
以上的种种奇怪原因在于没有考虑PRI，PRI值的纳入正是为了避免出现条件组态的存在与否都会导致结果这样的事情发生。所以在筛选组态时，必须要纳入PRI值。
以下顺序按照PRI阈值从低到高排列：
(1)，PRI值不能低于0.5，低于0.5表明实质上的不一致，所以0.5可以当作一个PRI阈值。
configurations with PRI scores below 0.5 indicate significant inconsistency.
Greckhamer, T., Furnari, S., Fiss, P. C., & Aguilera, R. V. (2018). Studying configurations with qualitative comparative analysis: Best practices in strategy and organization research. Strategic Organization, 16(4), 482-495.
（2）其次是PRI＞0.6这个阈值
A sufficiency analysis was conducted by using a frequency benchmark ≥ 1, raw consistency ≥ 0.80, and proportional reduction in inconsistency (PRI) cutoff ≥ 0.60.
Ding, H. (2022). What kinds of countries have better innovation performance?–A country-level fsQCA and NCA study. Journal of Innovation & Knowledge, 7(4), 100215.
（3）然后是PRI＞0.65 这个阈值
I then conducted sufficiency analyses using Ragin’s (2008) truth table algorithm to identify attribute combinations consistently linked to an outcome, applying a consistency benchmark of ≥ 0.8 (Ragin, 2006, 2008) complemented by a proportional reduction in inconsistency (PRI) score benchmark of ≥ 0.65 to avoid simultaneous subset relations of attribute combinations in both the outcome and its absence;
这里Greckhamer也解释了为啥要用PRI阈值，就是避免同时性子集关系，跟我前面讲的是一样的。
Greckhamer, T. (2016). CEO compensation in relation to worker compensation across countries: The configurational impact of country‐level institutions. Strategic Management Journal, 37(4), 793-815.
（4）之后是0.7这个阈值
In fuzzy set analysis, it is also important to consider PRI (proportional reduction in inconsistency) scores to avoid simultaneous subset relations of configurations in both the outcome and its absence. PRI consistency scores should be high and ideally not too far from raw consistency scores (e.g. 0.7);
来源于之前的定下PRI最低阈值的同一篇文献：
Greckhamer, T., Furnari, S., Fiss, P. C., & Aguilera, R. V. (2018). Studying configurations with qualitative comparative analysis: Best practices in strategy and organization research. Strategic Organization, 16(4), 482-495.
（5）最后是0.75这个阈值
Estimating a series of solutions with acceptable proportional reduction in consistency (PRI) values that exceeded0.75 served to determine an appropriate cutoff point for our consistency measure.
Frambach, R. T., Fiss, P. C., & Ingenbleek, P. T. (2016). How important is customer orientation for firm performance? A fuzzy set analysis of orientations, strategies, and environments. Journal of Business Research, 69(4), 1428-1436.
（6）也可以采用自然截断产生的PRI阈值
Second, if there is a break point in which the consistency significantly drops between two rows from a row with a high level of consistency to a row with the next level consistency, then the break point can be a cutoff for the high performance group.......
For example, in the healthcare industry, for financial performance, there is a significant drop in the consistency between the fifth row with a consistency of 0.91 to the sixth row with the next level of consistency, 0.82. Also, we use PRI consistency as a complementary measure for raw consistency. For the case with a raw consistency value of 0.82 in Table C1 for financial performance, its PRI consistency is far lower, compared to cases with a raw consistency of above 0.9
Park, Y., & Mithas, S. (2020). Organized Complexity of Digital Business Strategy: A Configurational Perspective. MIS Quarterly, 44(1).
（7）最后的最后要引用一下Pappas 和 Woodside 的QCA使用指导文章的几句话了。这篇文章总结得相当全，从原理到校准到各种阈值，甚至连软件操作步骤都给了出来，实属良心论文，比你导师不知道高到哪里去了。
PRI consistency is used to avoid simultaneous subset relations of configurations in both the outcome and the absence of the outcome (i.e., negation). PRI consistency scores should be high and close to raw consistency scores (e. g., 0.7), while configurations with PRI scores below 0.5 indicate significant inconsistency (Greckhamer et al., 2018). Thus, a PRI consistency threshold should also be used.
在fsQCA的概要表中，他们把PRI阈值定为0.5到0.7（可高于0.7），意思是别低于0.5就行了。
Close to “Raw consistency” (~0.70) > 0.50 minimum (Greckhameret al., 2018)
Pappas, I. O., & Woodside, A. G. (2021). Fuzzy-set Qualitative Comparative Analysis (fsQCA): Guidelines for research practice in Information Systems and marketing. International Journal of Information Management, 58, 102310.
而且我觉得他们的总结性表格做的相当全面，涵盖了fsQCA中从校准到真值表删选的所有的阈值，顺手复制粘贴一下：
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