Reconsidering Bipolar Scales Data As Compositional Data Improves Psychometric Healthcare Data Analytics

Abstract

Correct psychometric profiling and the choice of adequate therapeutic measures are the basis of any psychotherapeutic treatment. The preparation of a correct psychological profile benefits the patient and saves time and costs. Regarding psychometric questionnaires it is common practice to consider data of bipolar scales as interval scaled. This paper reveals the true compositional data structure (namely the Simplex) with respect to the psychometric limit of quantification of bipolar traits and constructs. The Simplex heavily affects the set of statistical procedures applicable. Disregarding the Simplex causes serious bias and results in erroneous standards and standard deviations, biased correlations, reduced convergent validity and a loss of statistical power. In this paper, the isometric log-ratio (ilr) transformation is suggested. It transforms Simplex data towards the interval scale and provides unbiased results, e.g., standards. By means of a simulation study, this paper shows that up to an 18\% increase in the statistical power of the well-known correlation test based on Student's t-distribution can be achieved. As the statistical power increases the sample size of psychometric studies can be reduced resulting in lower data collection costs. Besides economic and psychotherapeutic aspects, the results of the simulation study generalize from correlation analysis towards a larger set of standard statistical procedures. For example, testing the hypothesis of equality of the two means of independent samples using a t-test based on Student's t distribution is equivalent to testing the hypothesis of a null-correlation between the binary grouping variable and the dependent variable. Furthermore, the coefficient of correlation contributes to the slope of a regression line. Thus, the ilr approach also affects linear regression techniques.