Spatial Regression Models for the Social Sciences. Jun Zhu
spatial thinking and theories have originated largely from human geography and regional science. Space and place are in the “blood” of human geographers and regional scientists, who almost always consider space and/or place in their research. They provide the core spatial theories and use them to investigate and explain a wide range of social phenomena. Some spatial thinking and theories have been developed in other social science disciplines but not as extensively as in human geography and regional science. Most existing empirical studies of spatial social sciences, although conducted in a variety of social science disciplines, cite the work of human geography and regional science.
Second, spatial methodologies have been developed by human and physical geographers, regional scientists, economists, statisticians, and others. These methodologies, which are discussed in Section 1.2, include spatial analysis techniques such as GIS and remote sensing image processes as well as statistical methods for spatial data analysis such as spatial point pattern analysis, lattice (or areal) data analysis (where the spatial regression models and methods described in this book fall), geostatistics, and spatial interactive data analysis. The development of spatial methodologies enables and facilitates spatial thinking and theories to be applied to empirical studies of social science research.
Third, the application of spatial thinking and methodologies has experienced a rapid increase in the past two decades in many social science disciplines and subdisciplines (other than geography and regional science), including anthropology; criminology; demography; economics; political science (international studies, political economy, public administration); urban studies and urban planning; sociology; and interdisciplinary areas (such as area studies, development studies, environmental studies, and public health). Their data, when geographically referenced, can be analyzed using spatial methods. The rise in the application of spatial thinking and methodologies in these disciplines is largely due to the increased availability of geographically referenced data (i.e., spatial data), more user-friendly software packages for analyzing spatial data, and the rapid advances in robust and affordable computing power, as previously discussed.
Finally, spatial thinking and methodologies are seen as potentially beneficial to the humanities and social sciences such as communication, education, history, law, linguistics, and psychology from at least two perspectives. One, at the individual level, the socioeconomic and physical environments where the individual is located have effects on the individual; these environments can be seen as the “spatial” elements. Two, if individuals or observations are geocoded, which becomes increasingly easy to do with the development of geocoding techniques, the spatial dimension could be incorporated into empirical analysis using spatial methodologies. As a matter of fact, spatial thinking has already been developed in or for the disciplines of communication, history, and linguistics. Refer to the CSISS Classics for the relevant work.
It should be noted that the discussion here on spatial social science research is far from complete; rather, it is limited to our incomplete understanding of fields outside our own areas of expertise. Many books, journal issues, book chapters, journal articles, and websites provide overviews of spatial social science research. We suggest that readers look into these resources as well as spatial social science research in their own disciplines, if available, for more comprehensive understanding of spatial thinking and theories, methodologies, and applications.
1.2 Introduction to Spatial Effects
What are spatial effects, spatial analysis, spatial data analysis, spatial statistics, spatial autocorrelation, spatial dependence, and spatial heterogeneity? A newcomer to spatial regression models could easily be confused by the numerous concepts and terminologies associated with the models. This section introduces concepts related to spatial effects and the relevant terminologies used in the existing literature. We organize these concepts and terminologies into two categories:
Spatial analysis versus spatial data analysis versus geographic analysis
Four types of spatial data analyses
1.2.1 Spatial Analysis, Spatial Data Analysis, and Geographic Analysis
Spatial data refer to data that are geographically referenced and represent phenomena that are located in space. More specifically, spatial data refer to data that not only have the values or attributes related to the phenomena of interest but also the geographical or locational information of the observations. While aspatial data analysis uses only the former, spatial data analysis uses both. In a broad sense, spatial data analysis is the quantitative study of spatial data (Bailey & Gatrell, 1995). Spatial analysis is sometimes used interchangeably with spatial data analysis, geographic analysis, spatial information analysis, and geographic information analysis in the existing literature. While these terms refer to different things and have different foci, the boundary among them is somehow not clear and not completely agreed upon among researchers from different disciplines. For the purposes of this book, we understand spatial analysis as being composed of spatial data analysis and geographic analysis. The spatial regression models and methods are a specific set of tools for spatial data analysis.
Spatial data refer to data that are referenced geographically and represent phenomena located in space.
Spatial data analysis describes, models, and explains spatial data, from which we can make inferences about the phenomena under study and make predictions for areas where observations have not been sampled (Bailey & Gatrell, 1995). A spatial data analysis is conducted instead of aspatial data analysis if the data have spatial information and the spatial arrangements in the data or in the interpretation of the results are given explicit consideration. In particular, spatial data analysis is about using statistical methods to analyze spatial data; in the existing literature, this is often referred to as spatial statistics.
Spatial data analysis describes, models, and explains spatial data and enables us to make inferences and predictions.
Geographic analysis (or geographic information analysis or spatial information analysis) examines spatial data locations, attributes, and feature relations using geographic analysis techniques, and it also extracts or creates new information from spatial data (O’Sullivan & Unwin, 2010). Examples of geographic analysis are spatial overlay, spatial interpolation, network analysis, three-dimensional analysis, geocoding, terrain analysis, and others by using GIS software (e.g., ESRI) that uses GIS and remote sensing images. Geographic analysis methods and tools have been developed mostly by geographers, geologists, and environmental scientists and have been used by researchers from a wide range of fields.
Geographic analysis extracts or creates new information from spatial data and examines spatial data locations, attributes, and feature relations.
1.2.2 Four Types of Spatial Data Analysis
There are four types of spatial data analysis as categorized in existing spatial statistics and spatial econometrics literature (see, e.g., Bailey & Gatrell, 1995; Cressie, 1993; Schabenberger & Gotway, 2005; Waller & Gotway, 2004):
spatial point pattern analysis,
areal data analysis,
geostatistics, and
spatial interactive data analysis.
Each of these types of analysis has its own set of objectives and approaches.
Spatial point patterns (or spatial point processes) consist of the locations of events occurring in a spatial domain of interest (see, e.g., Baddeley, Rubak, & Turner, 2015; Cressie, 1993; Møller & Waagepetersen, 2003). A goal of spatial point pattern analysis often is to determine or quantify spatial patterns in the form of regularity or clustering (as deviation from randomness) or in relation to covariates. For example, disease mapping, for which the data often consist of locations of disease occurrences and are spatially referenced, is focused on the description and analysis of geographic variations in a disease (such as randomness, regularity, and clustering) and seeks explanations