`Truncate, replicate, sample': a method for creating integer weights for spatial microsimulation

Abstract: Iterative proportional fitting (IPF) is a widely used method for spatial microsimulation. The technique results in non-integer weights for individual rows of data. This is problematic for certain applications and has led many researchers to favour combinatorial optimisation approaches such as simulated annealing. An alternative to this is integerisation' of IPF weights: the translation of the continuous weight variable into a discrete number of unique orcloned' individuals. We describe four existing methods of integerisation and present a new one. Our method --- truncate, replicate, sample' (TRS) --- recognises that IPF weights consist of bothreplication weights' and `conventional weights', the effects of which need to be separated. The procedure consists of three steps: 1) separate replication and conventional weights by truncation; 2) replication of individuals with positive integer weights; and 3) probabilistic sampling. The results, which are reproducible using supplementary code and data published alongside this paper, show that TRS is fast, and more accurate than alternative approaches to integerisation.