Fig 1.

Residential histories as space–time step functions. The axes x and y define a geographic domain (e.g. longitude and latitude decimal degrees), the t axis represents time (e.g. date). The study extends from time t₀ to time t_T. The residential histories for persons i and j are shown as step functions through space–time. For example, person i begins the study residing at location x_i, y_i, t₀. They remain at that geographic coordinate until the instant before time t₁, when they move to x_i, y_i, t₁. The duration of time they reside at this first place of residence is ω₀.