Korneev Aleksei A, Krichevets Anatoly N, Sugonyaev Konstantin V, Ushakov Dmitriy V, Vinogradov Alexander G, Fomichev Aram A
Lomonosov Moscow State University, Moscow, Russia.
Institute of Psychology of Russian Academy of Sciences, Moscow, Russia.
Psychol Russ. 2021 Mar 31;14(1):86-100. doi: 10.11621/pir.2021.0107. eCollection 2021.
Spearman's law of diminishing returns (SLODR) states that intercorrelations between scores on tests of intellectual abilities were higher when the data set was comprised of subjects with lower intellectual abilities and vice versa. After almost a hundred years of research, this trend has only been detected on average.
To determine whether the very different results were obtained due to variations in scaling and the selection of subjects.
We used three methods for SLODR detection based on moderated factor analysis (MFCA) to test real data and three sets of simulated data. Of the latter group, the first one simulated a real SLODR effect. The second one simulated the case of a different density of tasks of varying difficulty; it did not have a real SLODR effect. The third one simulated a skewed selection of respondents with different abilities and also did not have a real SLODR effect. We selected the simulation parameters so that the correlation matrix of the simulated data was similar to the matrix created from the real data, and all distributions had similar skewness parameters (about -0.3).
The results of MFCA are contradictory and we cannot clearly distinguish by this method the dataset with real SLODR from datasets with similar correlation structure and skewness, but without a real SLODR effect. The results allow us to conclude that when effects like SLODR are very subtle and can be identified only with a large sample, then features of the psychometric scale become very important, because small variations of scale metrics may lead either to masking of real SLODR or to false identification of SLODR.
斯皮尔曼收益递减定律（SLODR）指出，当数据集由智力水平较低的受试者组成时，智力能力测试分数之间的相互关系更高，反之亦然。经过近百年的研究，这种趋势仅在平均水平上被发现。
确定是否由于量表缩放和受试者选择的差异而获得了截然不同的结果。
我们使用了三种基于调节因子分析（MFCA）的SLODR检测方法来测试真实数据和三组模拟数据。在后一组中，第一组模拟了真实的SLODR效应。第二组模拟了不同难度任务密度不同的情况；它没有真实的SLODR效应。第三组模拟了对不同能力受访者的偏态选择，也没有真实的SLODR效应。我们选择模拟参数，使模拟数据的相关矩阵与从真实数据创建的矩阵相似，并且所有分布都具有相似的偏度参数（约-0.3）。
MFCA的结果相互矛盾，我们无法通过这种方法清楚地将具有真实SLODR的数据集与具有相似相关结构和偏度但没有真实SLODR效应的数据集区分开来。结果使我们得出结论，当像SLODR这样的效应非常微妙且只能通过大样本识别时，心理测量量表的特征就变得非常重要，因为量表指标的微小变化可能导致真实SLODR的掩盖或SLODR的错误识别。
