Analyzing Lattice Data

Abstract

This chapter introduces procedures available in S+SpatialStats for analyzing and modeling lattice data. Lattice data are observations from a random process observed over a countable collection of spatial regions, and supplemented by a neighborhood structure. The observation locations can be regular (equally spaced grid) or irregular, and data at a particular location typically represent the entire region. The data observed at each site may be continuous or discrete. For example, the sample data frame sids contains rates of Sudden Infant Death Syndrome (SIDS) for each North Carolina county for the time periods 1974–1978 (Cressie and Chan, 1989). The locations are the coordinates of the county seats. This is discrete data residing on an irregular lattice with each site representing an entire county. For a more rigorous definition of lattice data, see chapter 1.

Before modeling the spatial component of lattice data in S+SpatialStats, we assume stationarity (see Glossary for definition) and multivariate normality of the data. This means that trend must be removed, and transformations may be required to stabilize the variance and/or to approximate normality. In section 3.3, basic exploratory data analysis (EDA) techniques were used to check these assumptions on the SIDS data. We will use the results of that preliminary analysis and expand on it throughout this chapter.

In this chapter you will learn to do the following tasks in S+SpatialStats:

• Define spatial neighbors (section 5.1).

• Test lattice data for spatial autocorrelation (section 5.2).

• Model lattice data using spatial regression (section 5.3).

• Simulate lattice data (section 5.4).