GLM for partially pooled categorical predictors with a case study in biosecurity

National governments use border information to efficiently manage the biosecurity risk presented by travel and commerce. In the Australian border biosecurity system, data about cargo consignments are collected from records of directions: that is, the records of actions taken by the biosecurity regulator. This data collection is complicated by the way directions for a given entry are recorded. An entry is a collection of import lines where each line is a single type of item or commodity. Analysis is simple when the data are recorded in line mode: the directions are recorded individually for each line. The challenge comes when data are recorded in container mode, because the same direction is recorded against each line in the entry. In other words, if at least one line in an entry has a non-compliant inspection result, then all lines in that entry are recorded as non-compliant. Therefore, container mode data creates a challenge for estimating the probability that certain items are non-compliant, because matching the records of non-compliance to the line information is impossible. We develop a statistical model to use container mode data to help inform biosecurity risk of items. We use asymptotic analysis to estimate the value of container mode data compared to line mode data, do a simulation study to verify that we can accurately estimate parameters in a large dataset, and we apply our methods to a real dataset, for which important information about the risk of non-compliance is recovered using the new model.