K-aggregated transformation of discrete distributions improves modeling count data with excess ones

The excess one pattern in count data has been documented in ecology but it has not been explicitly modeled or examined. In this study, we introduce a k-aggregated transformation of discrete distributions to better model count data with excess ones in a Bayesian generalized linear model framework and demonstrate its use with two groups of case studies (group 1: seabird bycatch in longline fisheries and Legionnaires disease incidence; group 2: survey abundance of Leadbeater’s possum and Frigatebird nesting sites). Group 1 examples have a clear excess one data pattern, and these examples are used to demonstrate the concept of the k-aggregation technique. On the other hand, group 2 examples lack a clear excess one pattern, and a modeler may not be motivated enough to use the k-aggregation technique in these cases. Nonetheless, k-aggregated transformation demonstrated better performance for both groups of examples. In all our case studies, the excess zero pattern co-occurred with an excess one pattern, and the excess zeros were modeled thorough either a zero-inflated or hurdle configuration. The better performance of k-aggregated distributions is due to their flexibility of adapting to the relatively high frequency of singletons in the data sets. This new technique has broad applicability and utility in improving modeling count data with potential excess ones.