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Abstract：
Bipolar psychometric scales data are widely used in psychologic healthcare. Adequate psychological profiling benefits patients and saves time and costs. Grant funding depends on the quality of psychotherapeutic measures. Bipolar Likert scales yield compositional data because any order of magnitude of agreement towards an item assertion implies a complementary order of magnitude of disagreement. Using an isometric log-ratio (ilr) transformation the bivariate information can be transformed towards the real valued interval scale yielding unbiased statistical results increasing the statistical power of the Pearson correlation significance test if the Central Limit Theorem (CLT) of statistics is satisfied. In practice, however, the applicability of the CLT depends on the number of summands (i.e., the number of items) and the variance of the data generating process (DGP) of the ilr transformed data. Via simulation we provide evidence that the ilr approach also works satisfactory if the CLT is violated. That is, the ilr approach is robust towards extremely large or infinite variances of the underlying DGP increasing the statistical power of the correlation test. The study generalizes former results pointing out the universality and reliability of the ilr approach in psychometric big data analysis affecting psychometric health economics, patient welfare, grant funding, economic decision making and profits.
摘要：
双极心理测量量表数据广泛用于心理保健。充分的心理分析有益于患者并节省时间和成本。赠款资金取决于心理治疗措施的质量。双极Likert缩放产量组成数据，因为对项目断言的任何数量级的协议都意味着分歧的互补数量级。如果满足统计的中心极限定理（CLT），则使用等距对数比（ilr）变换，可以将双变量信息转换为实值区间尺度，从而产生无偏统计结果，从而增加皮尔逊相关显著性检验的统计功效。在实践中,然而,CLT的适用性取决于求和的数量(即，项的数量)和ilr转换数据的数据生成过程(DGP)的方差。通过模拟，我们提供了证据，证明如果违反了CLT，ilr方法也可以令人满意地工作。也就是说,ilr方法对基础DGP的极大或无限方差是稳健的，增加了相关检验的统计能力。该研究概括了以前的结果，指出了心理测量大数据分析中ilr方法影响心理测量健康经济学的普遍性和可靠性，患者福利,赠款资金，经济决策和利润。
