Spatial Regression Models for the Social Sciences. Jun Zhu
has seventy-two counties, and the MCDs are county subdivisions. They are exhaustive political territories that are mutually exclusive and nonnested. Wisconsin is composed of some large cities and surrounding neighboring suburbs; multiple small villages, towns, and cities; and low-density rural areas. It is therefore a typical MCD state.
In Wisconsin from 1970 to 2010, the MCD boundaries were unstable—over time, boundaries of existing MCDs shift, new MCDs are created, former MCDs disappear, the names of MCDs change, and the jurisdictional statuses of the MCDs change (e.g., towns become villages and villages become cities). Changes such as these required that we adjust the data to establish a data set that is spatially consistent over time. We applied three rules: new MCDs are merged into the original MCDs from which they emerged; disappearing MCD problems are solved by dissolving the original MCDs into their current “home” MCDs; and occasionally, several distinct MCDs are dissolved into one super-MCD. The adjustments resulted in a data set of 1,837 MCDs. Among these, the sizes of the MCDs range from 0.1 to 368 square miles, with an average size of 29.6 square miles. In 2010, the populations of MCDs ranged from 40 to 594,833 persons, with an average population of 3,097 persons.
For the purpose of illustrating spatial regression models dealing with spatial heterogeneity, in Sections 5.1 and 5.2, we further classify the MCDs into rural, suburban, and urban areas. Many classifications of rural, suburban, and urban areas have been used in existing research, and a single, standard classification does not exist (Chi, 2012). Our classification in this book is based on the 2000 Census Urban Areas and 2000 Metropolitan and Micropolitan Statistical Areas (MMSAs) defined by the U.S. Office of Management and Budget. Our classification system consists of the following: MCDs that fall into the Census Urban Areas we call urban areas, MCDs that fall into the MMSAs but not into the Census Urban Areas we call suburban areas, and MCDs that fall out of both the MMSAs and the Census Urban Areas we call rural areas (Figure 1.3). This categorization may be useful for evaluation purposes but does not necessarily accurately reflect the actual conditions in Wisconsin.
Figure 1.3 ⬢ The classification of rural, suburban, and urban MCDs in Wisconsin
Source: Chi (2012).
Studying population change at the MCD level has two advantages. The first one is the relevance of MCDs to planning and public policy making. In most parts of Wisconsin, census tracts have average sizes similar to MCDs and may serve as an alternative spatial unit of analysis. However, census tracts are geographic units delineated by the U.S. Census Bureau and do not have specific political or social meanings. MCDs, on the other hand, are functioning governmental units. The second advantage is that studying population change at subcounty levels, such as the MCD level, can provide insights into possible local dynamics that may not be captured by analysis at the county level or higher. For example, changes in transportation accessibility may not have major impacts on population change at county levels or higher, but they may have great impacts at subcounty levels. The changes may offset each other when the local changes are aggregated from small areas to larger ones. The scale effect, as this phenomenon is known (Fotheringham & Wong, 1991), would be more obvious in an urban area, which has one or a few counties divided into several MCDs. An example from the existing literature is research revealing that highway expansion/construction may benefit neighborhoods a few blocks away from the work but might be unpleasant to those in the neighborhoods nearby (Chi & Parisi, 2011). Airport expansion is a similar situation, with the work benefiting areas not too far away but being unpleasant in nearby areas. In both cases, the neighborhoods that are not immediate would experience less population loss and potentially higher population growth than the immediate neighborhoods, but in the county as a whole, the total population change would not be affected much by the internal migration due to these situations. Using MCDs instead of counties or census tracts as the unit of measure can show such subtle changes in the associations of various variables with population change and provide insight for policy makers in the affected neighborhoods.
1.3.4 Population Change in Wisconsin
In our case study, population change in terms of population counts as reported by the U.S. Census Bureau is the response variable (or dependent variable) and is expressed as the natural log of population in a census year over the population ten years earlier. For example, the measure of the growth rate from 2000 to 2010 is the natural log of the 2010 population divided by the 2000 population. This measure of population change helps achieve a normal “bell-shaped” distribution; makes interpreting the population change rate easier (growth is shown by a positive value, decline is shown by a negative value, and no change at all is shown by zero); and accounts for initial population size (Chi, 2009). The population data for this case study are provided by decennial U.S. Census Bureau censuses from 1970 to 2010.
Figure 1.4 shows population change in Wisconsin in four time periods: 1970–1980, 1980–1990, 1990–2000, and 2000–2010. From 1970 to 1980, relatively high population growth occurred in rural and suburban areas. The 1970s marked a rural renaissance for the first time in Wisconsin, also called “turnaround migration” by rural demographers, as natural amenities and employment opportunities attracted migrants to the amenity-rich rural areas (Johnson, 1999). During this time, rural and suburban MCDs experienced higher population growth rates than urban MCDs: the average population growth rate was 13.4 percent for rural MCDs, 16.5 percent for suburban MCDs, and 11.7 percent for urban MCDs (Table 1.1).
Figure 1.4 ⬢ Population change at the MCD level in 1970–1980, 1980–1990, 1990–2000, and 2000–2010 in Wisconsin
Table 1.1
Note: The numbers in each cell represent the average population change rate at the MCD level. Standard deviations are in parentheses.
From 1980 to 1990, a majority of MCDs experienced population decline; it was the slowest growth decade in the history of Wisconsin. The population redistribution pattern was renewed metropolitan growth, mainly due to economic disruptions such as the farm debt crisis, deindustrialization (which downsized the manufacturing), and urban revival (which stopped people migrating to rural areas). In this decade, the average population growth rate in urban MCDs (6.3 percent) was much higher than that in suburban MCDs (3.8 percent), which was much higher than that in rural MCDs (0.1 percent).
From 1990 to 2000, rural areas rebounded as an improved economy and the areas’ natural amenities attracted retirees. Relatively high population growth occurred in northern Wisconsin, central Wisconsin, and some suburban areas. The population growth rate of rural MCDs (9.1 percent) was similar to that of urban MCDs (10.6 percent), and the average population growth rate in suburban MCDs (13.1 percent) was relatively higher than those in rural and urban MCDs.
From 2000 to 2010, the population redistribution pattern was selective deconcentration; technological innovations in communications and transportation, companioned with the economic crisis that occurred in 2008, made migration more selective. It appears that population growth occurred mostly in suburban areas. The average population growth rate of MCDs from 2000 to 2010 in Wisconsin was 3.6 percent. The growth rate varies spatially along the urban-rural continuum: the average population growth rate was 1.8 percent in rural MCDs, 9 percent in suburban MCDs, and 6.1 percent in urban MCDs.
1.4 Structure of the Book
Throughout this book, each spatial regression method is introduced in two components. First, we explain what the method is and when we can or should use it by connecting it to a few social science research topics. Mathematical formulas and symbols are kept to a minimum. Second, we use three social science examples to demonstrate how to use the method and what the results can tell us. The primary example, which is the same research and data for most methods discussed in the book, examines