Knox meets Cox: adapting epidemiological spatial statistics to demographic studies

Carl P. Schmertmann, Florida State University
Renato M. Assuncao, Universidade Federal de Minas Gerais
Joseph E. Potter, University of Texas at Austin

Many important questions and theories in demography focus on how events cluster in space and time. Space-time analysis has always been important in studying fertility transition, for example, but with few exceptions demographers have not used formal statistical methods to describe and analyze time series of maps. One formal method, used widely in epidemiology, is Knox's space-time interaction test. We discuss the potential of the Knox clustering test in demographic research, note some possible pitfalls, and demonstrate how to use familiar proportional hazards models to adapt the Knox test for demographic applications. These adaptations allow for non-repeatable events, and for the incorporation of structural variables that change in space and time. We apply the modified test to data on fertility decline in Brazil over 1960-2000, and show how the modified method can produce maps showing where and when diffusion effects and clustering seem strongest, net of covariate effects.