KSTSE procedure

Calculates the standard error for the space-time K function (D.A. Murray, P.J. Diggle & B.S. Rowlingson).

Option

PRINT = string

Controls printed output (summary); default summ

Parameters

Y = variates

Vertical coordinates of the spatial point patterns; no default - this parameter must be set

X = variates

Horizontal coordinates of the spatial point patterns; no default - this parameter must be set

TIMES = variates

Times for each event

YPOLYGON = variates

Vertical coordinates of the polygons; no default - this parameter must be set

XPOLYGON = variates

Horizontal coordinates of the polygons; no default - this parameter must be set

S = variates

Vectors of distances to use; no default - this parameter must be set

TVALUES = variates

Time scales for the analysis

TLOWER = variates

Lower temporal domain

TUPPER = variates

Upper temporal domain

SE = variates

Saves the standard errors

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. KSTSE calculates the standard error for the space-time K function.

The data required by the procedure are the coordinates of a spatial point pattern (specified by the parameters X and Y), and the times for each of the events (specified by TIMES). The coordinates of a polygon containing the spatial points are specified by the parameters XPOLYGON and YPOLYGON, and the parameter S is used to supply the vector of distances at which to calculate the spatial K function. The TLOWER and TUPPER parameters specify the start and finish of the temporal range. The TVALUES parameter is used to supply the vector of times at which to calculate the temporal K function. The output of the procedure are vectors of estimates of the spatial and temporal K function corresponding to the distances in S and times in TIMES. The standard errors of the space-time interaction can be saved using the SE parameter.

Printed output is controlled using the PRINT option. The default setting of

summary prints the standard errors for the space-time clustering.

Option: PRINT.

Parameters: Y, X, TIMES, YPOLYGON, XPOLYGON, S, TVALUES, TLOWER, TUPPER, SE.

Method

A procedure PTCHECKXY is called to check that X, Y and TIMES have identical restrictions. A similar check is made on XPOLYGON and YPOLYGON. The procedure then calls PTCLOSEPOLYGON to close the polygon specified by XPOLYGON and YPOLYGON. The SORT function is then used to create variates containing the distances in S and time in TVALUES arranged into ascending order. (The original variates are left unchanged.) The procedure then calls a procedure PTPASS to call a Fortran program to calculate an estimate of the space-time clustering standard errors.

References

Diggle, P,J. (1983). Statistical Analysis of Spatial Point Patterns. Academic press, London.

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.