Patterns of item score and total score distributions on depression rating scales in the general population: evidence and mechanisms

Recent research has demonstrated that item scores and total scores on depression rating scales exhibit common distribution shapes in a general population. Specifically, responses to depressive symptom items show a proportional relationship between response options, except for the lower end option, whereas total scores exhibit an exponential distribution, except for the lower end of the distribution. The common mathematical distributions of item scores and total scores may help explain the scoring mechanism of a depression rating scale. This paper, therefore, discusses how the distribution shapes are generated. Two conditions are assumed: (1) each individual's latent degree of depression forms an exponential distribution in a general population, and (2) the threshold of each depressive symptom forms a normal distribution. A simulation study applying the two assumptions revealed that simulated total scores follow an exponential distribution through a strong linear relationship between an individual's latent trait of depression and simulated total scores. Furthermore, the strong linear relationship between total scores and the individual's latent trait of depression supports the prevailing view that total scores on a Likert type scale tend toward interval data. Regarding item scores, an analysis of boundary curves, which divide the distribution of total scores by each item score, revealed that the lower end option and the next option distances have a trade-off relationship, and the remaining option distances have a proportional relationship across all items. In conclusion, the assumption that a latent trait of depression follows an exponential distribution helps explain the mathematical pattern of item response and total score distribution. Furthermore, the item score and total score distribution shapes on depression rating scales may serve as evidence of the level of measurement.