Exponential distribution of total depressive symptom scores in relation to exponential latent trait and item threshold distributions: a simulation study.

When exponential distribution was set to the latent trait's random numbers and each item's threshold had a certain degree of standard deviation, simulated total depressive symptom scores showed a linear pattern except at the lowest end of scores with a log-normal scale. Our results suggest that total depressive symptom scores follow the distribution of the latent trait of depressive symptoms due to the property of ordinal scales, which is characterized by individual differences in the threshold of each item.