DKSTPLOT procedure

Produces diagnostic plots for space-time clustering (D.A. Murray).

Options

PLOT = string

Whether to produce plots separately or in composite (separate, combined); default comb

DZERO = string

Whether to produce a DZERO plot (yes, no); default no

Parameters

Y = variates

Vertical coordinates of the spatial point patterns

X = variates

Horizontal coordinates of the spatial point patterns

KS = variates

Estimates of spatial K function

KT = variates

Estimates of temporal K function

KST = matrices

Estimates of space-time K function

KSE = matrices

Estimates of standard errors of space-time K function

Description

For data that consist of locations and times of events within a specified spatial region and time-period, it is often of interest to examine whether events that are relatively close in space are also relatively close in time. Data that have events both close in space and time are said to exhibit space-time clustering. DKSTPLOT produces three diagnostic plots for space-time clustering. The first plot is a map of the spatial point pattern. The second is a contour or perspective plot of the difference between the space-time K function and product of the spatial and temporal K functions.

D^(s,t) = K^st(s,t) - K^s(s) × K^t(t)

This gives information on the scale and nature of the dependence between spatial and temporal components. Alternatively, by setting the option DZERO=yes the contour plot will be drawn by scaling D^(s,t) by the product of the spatial and temporal K functions.

D0^(s,t) = D^(s,t) / K^s(s) × K^t(t)

This represents the proportional increase attributable to space-time interaction. The third plot is of the standardized residuals given by

(K^st(s,t) - K^s(s) × K^t(t)) / SE(K^st(s,t))

The data required by the procedure are the coordinates of a spatial point pattern (specified by the parameters X and Y). The estimates for the spatial and temporal K functions are supplied using the KS and KT parameters. The space-time K function estimates and associated standard errors are supplied using the KST and KSE parameters.

The PLOT option controls whether to display the plots on one graph or to produce a separate graph for each plot.

Options: PLOT, DZERO.

Parameters: Y, X, KS, KT, KST, KSE.

Method

The procedure DPTMAP is called draw the map of the spatial point process. The estimates for the K functions and associated standard errors are calculated using the procedures KSTHAT and KSTSE.

Action with RESTRICT

The variates X and Y may be restricted. The K function estimates cannot be restricted.

References

Diggle, P.J., Chetwynd, A.G., Haggkvist, R. & Morris, S.E. (1995). Second-order analysis of space-time clustering. Statistical Methods in Medical Research, 4, 124-136.