This is the first of five chapters on "Spatial Modeling I" from the user manual for CrimeStat IV, a spatial statistics package that can analyze crime incident location data.
This chapter, "Kernel Density Interpolation," discusses tools that interpolate incidents by using the kernel density approach. "Kernel Density Interpolation" is a technique for generalizing incident locations to an entire area. Whereas the spatial distribution and hot-spot statistics provide statistical summaries for the data incidents themselves, interpolation techniques generalize those data incidents to the entire region. Specifically, they provide density estimates for all parts of a region. The density estimate is an intensity variable, a Z-value, that is estimated at a particular location. Consequently, it can be displayed by either surface maps or contour maps that show the intensity at all locations. Although there are many interpolation techniques, "kernel density estimation" is an interpolation technique that is appropriate for individual point locations (Silverman, 1986; Hardles, 1991; Bailey & Gatrell, 1995; Burt & Barber, 1996; Bowman & Azalini, 1997). Kernel density estimation involves placing a symmetrical surface over each point, evaluating the distance from the point to a reference location based on a mathematical function, and summing the value of all the surfaces for that reference location. This procedure is repeated for all reference locations. CrimeStat has two kernel density interpolation routines. The first applies to a single variable, and the second pertains to the relationship between two variables. Each of these routines is described in this chapter. The chapter also reviews the advantages and disadvantages of kernel density interpolation. Nine attachments present papers by various authors that describe how kernel density interpolation is used to address a variety of situations in diverse settings. 26 references and extensive figures that include computer screens and maps from examples