Duration Modeling of Spatial Point Patterns

Abstract

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete‐state, continuous‐time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.