Modeling cargo clearance duration at Kenyan borders using multilevel survival models

Abstract

Nested data is often encountered in survival applications, for instance when analyzing the time to suffer a first heart attack for individuals who are nested within families and who are treated by the same doctor or the time to master a literacy skill for children nested in classrooms which are nested within schools. Indeed, multilevel survival models are the appropriate models to analyze durations that have a nested structure. This paper makes use of multilevel survival models to analyze cargo clearance durations at Kenyan borders. In the application, the dependent variable is the duration to release cargo, which is the time taken to release of the cargo since arrival. The explanatory variables include cargo weight, continent of cargo destination, cargo clearance year and customs regime, which is the regime that differentiates several types of cargo, including bonded warehousing cargo, export cargo, temporary importation cargo and transit regime. The multilevel survival models presented in this paper make use of the Cox proportional hazard model framework , which includes random effects in the models to denote the increase or decrease in hazard for distinct clusters. The theoretical framework of the two-level random coefficient models are discussed from a frequentist perspective. The Exponential and the Weibull distributions are the two choices for the baseline hazard function. Moreover, the categorical variable ‘Worth of Cargo’ will be used as a nesting structure for the Kenyan cargo data, where individual cargoes (level-1 units) are clustered by their worth (level-2 units). All fitted multilevel models include a random intercept and a random slope for the cargo weight.