Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

Shannon's index is one of the measures of biodiversity, which is intended to quantify both richness and evenness of the species/individuals in the ecosystem or community. However, application of Shannon's index in the field of substance use among the street children has not been done till date.

This paper is concerned with methods of estimating Shannon's diversity index (SDI), which can be used to capture the variation in the population due to certain characteristics. Under the consideration that the probability of abundance, based on certain characteristics in the population, is a random phenomenon, we derive a Bayesian estimate in connection with Shannon's information measure and their properties (mean and variance), by using a probability matching prior, through simulation and compared it with those of the classical estimates of Shannon. The theoretical framework has been applied to the primary survey data of substance use among the street children in Delhi, collected during 2015. The measure of diversity was estimated across different age profiles and districts.

The results unrevealing the diversity estimate for street children corresponding to each region of Delhi, under both the classical and Bayesian paradigms. Although the estimates were close to one another, a striking difference was noted in the age profile of children.

The Bayesian methodology provided evidence for a greater likelihood of finding substance-using street children, belonging to the lower age group (7-10, maximum Bayesian entropy-3.73), followed by the middle (11-14) and upper age group (15-18). Moreover, the estimated variance under the Bayesian paradigm was lesser than that of the classical estimate. There is ample scope for further refinement in these estimates, by considering more covariates that may have a possible role in initiating substance use among street children in developing countries like India.