Что такое экологические ошибки в рассказе

Solutions to the Ecological Inference Problem?

A second basic approach, described in a 1953 study by Duncan and Davis, is based on establishing bounds for the minimum and maximum possible for each cell of a cross-tabulation in each of the aggregate units. By summing these extrema up over the data set, it is possible to determine with 100% confidence the minimum and maximum bounds of the correlation that could obtain in the individual-level data.

In 1997, King proposed a “solution” to the ecological inference (EI) problem, the EI technique. It was also developed in the context of dichotomous dependent variables. The EI technique combines the method of bounds with the Goodman regression technique, and estimates the system using maximum likelihood and numerical simulation, assuming a bivariate normal distribution for the parameters. Critics, however, have pointed out a number of flaws with King’s technique, a review of which is beyond the scope of this essay. Important critiques were done by Anselin in 2000, Anselin and Cho in 2002, Freedman in 1998, and McCue in 2001.

In other words, the narrow focus of King’s technique is reconstructing a description of the individual data, not evaluating a causal model. This is an adequate goal in King’s motivating example, ascertaining voting patterns by race for the purpose of redistricting litigation. But in virtually any other social science application, our interest is in a causal model that cannot be reduced to a contingency table. Even in voting analysis, there are substantively interesting questions about whether racial identity affects voting net of other factors, such as income, occupation, and so on. Further, King readily acknowledges that his method will be less effective when the dependent variable is continuous, because no information is gleaned from bounds. These are rather important limitations.

Further discussions of approaches to reduce bias in ecological inference were provided by Achen and Shively in 1995, Cho in 2001, and Freedman in 1991 and 2002.

2 The Impact of the Ecological Fallacy on Research Practices

Although the term ecological fallacy is most often associated with W. S. Robinson, Robinson does not use the term in his classic 1950 article. Instead he uses the term ‘ecological correlation,’ and he states that his analysis ‘provides a definite answer as to whether ecological correlations can validly be used as substitutes for individual correlations. They cannot’ (Robinson 1950, p. 357). Robinson uses illiteracy data from the 1930 US census to show the discrepancy between ecological correlations and individual correlations. The correlation between percent black and percent illiterate is r=0.77 across States and r=0.95 across nine larger geographic divisions of the USA. The size of those ecological correlations stands in stark contrast to the size of the individual-level relationship between race (black vs. others) and illiteracy (r=0.20). As a second example, Robinson notes that the ecological correlation of percent foreign-born and percent illiterate across States is large and negative (r=−0.53), suggesting that the foreign-born are substantially less likely to be illiterate. Yet the foreign-born actually are more likely to be illiterate, as shown by the positive correlation at the individual level (r=0.12).

Whereas Robinson focused on the danger of using aggregate data to draw conclusions about the behavior of individual people, the ecological fallacy problem in fact applies to inferences across levels of aggregation in general. Individuals need not be people. The terms individual level and aggregate level as used here refer to relative levels of aggregation. To illustrate, the term ‘individual’ could refer to a single church congregation within a population of congregations. The ecological fallacy problem would arise if a researcher tried to use data on racial diversity and attendance growth rates across church denominations (collections of congregations) to draw conclusions about the effect of racial diversity on local church growth. Because parishioners attend a local congregation, it is racial diversity at the local level, not at the denomination level, that is the natural focus here. One could of course survey local congregations in this instance, but the survey would ask questions about a collective (a congregation) rather than about a person.

It would be difficult to overstate the impact Robinson’s article has had on social science research during the second half of the twentieth century. The use of ecological correlations to study individual-level relationships had been commonplace before Robinson’s article, and the article sharply curtailed that practice. The article also served to motivate the development of survey research. If aggregate data are not adequate to study individuals, then social scientists need data on individuals. One efficient way to gather data on individuals is to ask them questions. So in this way Robinson’s message about the need for individual-level data to study individuals no doubt played a role in the amassing of the large survey data sets that have become standard fare in social science research in the twenty-first century.

It is sometimes difficult or impossible to collect survey data to overcome the ecological fallacy problem, however, for two main reasons. First, individuals might be hard to reach. The extreme case of this occurs in historical research, where the pertinent individuals are dead. For this reason, historical research is especially plagued by the ecological fallacy problem (geography is another discipline especially affected, since geographic research is often based on spatial units). Aggregate data often are the only data available to historians, and it is not possible to go back in time to collect data to determine who voted for the Nazis, for example. Second, individuals might be reachable, but the needed information is sensitive. To protect the privacy of individuals, government agencies in some instances aggregate individual-level data before releasing the data to researchers (see Aggregation: Methodology). But aggregation in turn creates the risk that researchers using the aggregate data might commit the ecological fallacy.

The Ecological Fallacy

In 1950, Robinson coined the term ecological fallacy to refer to the error of interpreting variations in environmental settings as variations among individuals. One tactic for solving Robinson’s ecological fallacy is to construct surveys in which questions clearly state whether they are asking personal opinions of the subject or general assessments of an environment setting. A Likert scale example of an ecological (i.e., environmental) question is to ask respondents to agree or disagree with the comment, “Sometimes class is very disorganized.” A comparable example in which the individual is the unit of analysis is to ask respondents to agree or disagree with the comment, “Sometimes I am not prepared when I come to class.” The ecological question provides a generalized assessment of the environment without targeting the source of disorganization. In the ecological example, it is unclear as to what unit of analysis the subjects are responding to—the setting, the teacher, the other students, themselves, or all of these.

Richards and colleagues compared the use of individualist and ecological units to analyze classroom environments. They used the Classroom Environment Scales developed by Moos and Trickett, which consist of true–false questions about the classroom environment. Richards et al. (1991) noted that the questions were “modeled on and resemble the type of questions used in objective personality tests” (p. 425). Consequently, measures of dispersion (such as standard deviation) were much higher among individuals in settings than across settings and reliability measures (alpha) were also higher across than within settings. Richards et al. also suggested that assessments of setting measures were mediated by personality differences between the individuals and that this confounded the results within any one setting. Thus, survey questions should be crafted so that they distinguish and elicit assessments of the environmental setting rather than serve as “disguised measures of individual differences.”

Richards and colleagues use the terms ecology and settings interchangeably. However, it should be remembered that, strictly speaking, the setting is not the unit of analysis but the group that inhabits the setting. The actual classroom does not fill out a questionnaire, students do. The Richards et al. study is important because it unequivocally confirms that by themselves, and without a theoretical justification, individuals as the unit of analysis are invalid and unreliable units by which to measure setting-level characteristics. It should be noted that by “setting,” Richards et al. are referring to the small-scale groups that inhabit the setting and thus setting is a group-level unit. If the goal of the study is to understand the characteristics and dynamics of settings (in this case, the classroom), then the proper sample for the study is settings and not individuals, and the goal of the researcher is to examine variation between settings and not between individuals.

In 1997, Gary King proposed a statistical solution to the ecological inference problem. Leo Goodman had previously proposed an ecological regression model to estimate individual differences from census data. King added to Goodman’s model by using random coefficients to further minimize the aggregation bias. His solution has met with partial success in finding estimators of subpopulations within a larger population. However, although statistical sampling is a powerful tool, statistics is not good at low-level inferences—that is, reducing the whole to its components, a kind of reverse statistics.

The ecological fallacy is the error of attributing the characteristics of a population to an individual. Statistical inference is intended to generalize from a sample population to the whole population. The goal of statistics is to generalize from the particular to the whole and not from the whole to the particular. As such, statistics cannot offer a solution to the ecological fallacy. Data on individuals or on subpopulations within a larger population can best be obtained by ensuring that the unit of analysis is the individual or the subpopulation and not the larger population. As Richards and colleagues note, this problem can be avoided by designing survey instruments that elicit individual characteristics and attitudes. It is only from individualistic data that the researcher can track individual and subpopulation characteristics when necessary.

In a study in which local and individual hospitalization rates were derived from community-level estimates of various indicators of socioeconomic status (SES), Hofer noted that SES community profiles may not be representative of those individuals in the community who are actually going to the hospital. For example, it is known that the proportion of elderly who have medical coverage is far greater than it is for young adults, and that some of these elderly patients will use the hospital many times. To obtain accurate estimates of the subpopulations using and not using the hospital, it is necessary to obtain data on samples of individuals, not social aggregates. The best aggregate estimator of subpopulation or individual differences is to either ensure that the individual characteristics to be analyzed are representative of the aggregate or to use complete analytical models that target only that set of SES data pertinent to a target population. In their study on hospitalization rates, Billings et al. found it necessary to include age and income interactions in assessing SES variables in small area studies.

Although ecological (groups) units comprise individuals, their characteristics are not equivalent to those of the individuals in the group; therefore, one has to apply a different theory to studies that use collectivities as units of analysis than to studies that use the individual as the unit of analysis. When collectivities are the units of analysis, the proper subject of inquiry should be the overall characteristics and emergent properties of populations. Group-level characteristics may be very different from those of the individual members of the group. Ethnographic and psychological studies are frequently guilty of the opposite of the ecological fallacy: the fallacy of mapping individual characteristics onto a group. This problem, called the “individual differences fallacy” by Richards in 1990, is discussed next.

1.22.2.3 Spatial Extent: Continuous Surfaces and Raster Scale

Perhaps the disciplines that have addressed the problems of ecological fallacy related to geospatial data most directly have been ecology, natural resources, and remote sensing. Considerable research in these fields grapples with the particular issue of scale and scaling as it relates to the ability to use spatial data to link spatial patterns with natural processes (Blöschl, 1996; Hunsaker et al., 2013; Lowell and Jaton, 2000; Mowrer and Congalton, 2003; Quattrochi and Goodchild, 1997; Sui, 2009; Wu et al., 2006). Landscape processes do not always operate on the scales represented in geospatial data, yet the geospatial data we use in a GIS to assess these systems imposes a fixed scale within which we attempt to understand them. Especially in disciplines related to ecology and natural resources, spatial data analyses revolve around use of the raster data structure to represent continuous surfaces. The issue of spatial extent is exemplified by the grid cell structure and the scale it imposes on spatial analyses.

Placement of discrete boundaries impacts analyses and contributes uncertainty associated with derived results. This is considerable when using the raster data structure. Although rasters represent continuous surfaces, the grid cell structure itself imposes a discrete boundary and associated scale of representation. In the raster data structure, the spatial support or resolution of spatial datasets is predefined, determined by mechanisms of the satellite (in the case of remotely sensed imagery) or grid cell resolution (in the case of digital elevation models (DEMs)), without consideration of the natural processes that are evaluated using these data (Dark and Bram, 2007).

Continuous surfaces represent spatial features that are not discrete and commonly represented in a GIS using uniform grids. This raster grid cell resolution imposes a measurement scale on the nature of geospatial analyses and, by association, a scale on the process (e.g., hydrologic, ecologic) these data and associated analyses represent. The concept of resolution is closely related to scale and refers to the smallest distinguishable component of an object (Lam and Quattrochi, 1992; Tobler, 1988). The grid cell is also referred to as the spatial support, a concept in geostatistics referring to the area over which a variable is measured or predicted (Dungan, 2002). Spatial resolution is related to the sampling interval. The Nyquist sampling theory states that the sampling rate must be twice as fine as the feature to be detected. The sensitivity of model input parameters and model predictions to spatial support have been documented in numerous geospatial analyses and remains an important factor in our understanding, assessment, and quantification of uncertainty in spatial data and related modeling applications (Wechsler, 2007).

Practitioners often do not have control of the grid cell resolution of a dataset (e.g., products provided from satellite remote sensing or government-produced DEMs). Subgrid variability—that is variability at scales larger than those captured by the grid cell area—cannot be resolved or captured using a typical raster grid cell structure. This is changing as new technologies place the decision for selecting an appropriate support in the hand of the practitioners, such as data derived from UAV platforms.

As technologies advance, new spatial datasets are continually being developed. In recent years, the commercial availability of low-cost hardware and embedded computer systems has led to an explosion of lightweight aerial platforms frequently referred to as unpiloted aerial vehicles (UAVs) or “drones”. UAVs are becoming a powerful cost-effective platform for collection of remotely sensed images. Advances in computer vision software have enabled the construction of 3D Digital Surface Models (DSMs) from acquired imagery using Structure from Motion (SfM). SfM uses complex computer algorithms to find matching points from overlapping images, enabling reconstructions of surface feature reconstructions from overlapping 2D images (Fonstad et al., 2013; Westoby et al., 2012).

UAV-derived imagery and surfaces are cost effective, accessible, and facilitate data collection at spatial and temporal scales previously inaccessible. As such, they are becoming widely used data sources in a wide range of disciplines and applications including geomorphological mapping (Gallik and Bolesova, 2016; Hugenholtz et al., 2013), vegetation mapping (Cruzan et al., 2016), and coastal monitoring (Goncalves and Henriques, 2015). Point clouds obtained from SfM-derived surfaces are used to generate digital surface models (DSMs).

Data quality is addressed using RMSE to quantify the accuracy of UAV-derived surfaces and vertical accuracies in the centimeter range are commonplace (Harwin and Lucieer, 2012; Neitzel and Klonowski, 2011; Reshetyuk and Martensson, 2016; Verhoeven et al., 2012). However, statements of accuracy and data quality are no substitute for estimates of uncertainty and resulting decisions for fitness-of-use. Data quality and accuracy assessment have become mainstream practice. The challenge remains to bridge the gap between representation of data quality and mechanisms for quantifying and communicating uncertainty.

There is a long tradition, in the social and life sciences, of attempts to infer individual behavior from group behavior. Durkheim’s book on suicide is an early example. The ‘ecological fallacy’ consists of ascribing to individuals the characteristics of groups to which they belong, even though the relevant individuals may not share such characteristics. The issues are discussed in seminal papers by Robinson, Duncan and Davis, and Goodman, which are summarized here. Ecological regression is considered, along with recent work on random-coefficients models. Examples are drawn from epidemiology, voting rights, and survey data.

The Defendants’ Response

The defendants’ response to the plaintiffs’ evidence takes several forms. One is to argue that precinct-level data are not a valid basis for deriving the estimates reported. This often entails little more than a recitation of the ecological fallacy, which in this context states that we cannot draw inferences about the distributions of candidate preferences of the individuals within groups from data based on heterogeneous aggregations (precincts) of these groups. This response is rarely successful, however, in light of the pronounced differences usually observed across these aggregates.

A far more frequent response is to offer a different definition of what racially polarized voting entails, a definition under which such divisions are, by themselves, treated as irrelevant. Defendants often argue that if voting is to be considered polarized, it must be based on racial animus. Voting, in short, must be more than racially divided; it must also be racially motivated. Under this definition, group divisions in candidate preferences, no matter how acute or consistent, are not sufficient to establish polarized voting. Rather, additional evidence showing that these preferences were motivated by racial animus is required. This necessary condition, given this definition, is normally introduced by the testimony of an expert. At times, the jurisdictions simply argue that the burden of proving that racism is the causal factor, or at least a pronounced causal factor, rests with the plaintiffs. Experts called by defendants testify that the plaintiffs’ evidence of group divisions, no matter how pronounced and persistent the divisions may be, is simply descriptive and establishes at best correlation not causation. Without evidence of racial motivations behind the racial divisions, defendants argue, the plaintiffs must lose.

Racial divisions in voting patterns could be viewed, however, as establishing a reasonable presumption of polarized voting, even if racial animus is a definitional criterion. If this is the case, then a defendant jurisdiction must rebut this presumption through evidence of its own that shows the absence of racial animus. This requires that the defendants themselves provide evidence that demonstrates nonracial explanations for the divisions. This approach involves identifying variables other than the relative presence of a minority group’s voters across the precincts that might relate to the voters’ choices. Variables suggested to have this explanatory power include the party identifications of the voters, their incomes, the issues that concern them, and the geographical distance between the residences of candidates and the precincts within which voters reside—variables that themselves typically relate to the racial composition of the precincts.

These actual multivariate analyses deviate from the precinct-based analyses used to demonstrate racial divisions. Although some of the suggested variables can be directly measured at the precinct level for past elections, others such as the party identifications and issue concerns of voters cannot. The actual analysis therefore shifts to an examination, across elections, of the characteristics of candidates and their campaigns. The unit of analysis becomes elections, not precincts. Variables such as the party affiliation of the candidates (rather than the voters), their incumbency status, their name identification, the relative cost of their campaigns, and the race of the candidates are related to the outcomes of elections, measured by the overall percentage of the votes the various candidates received or simply whether the candidates won or lost. These analyses do not reveal whether or not the voters are divided along racial lines but, rather, whether the race of the candidate has a separate, independent effect on the outcome measures when the other variables are included. If it does not, it is argued, the divisions in candidate preference are cleansed of any racial content.

Another approach to the nonracial explanation argument has been employed recently. This approach does rely on the precinct as the unit of analysis. It involves attempting to measure the party identification of the voters in past elections at the precinct level and then comparing the bivariate correlation coefficient between that variable and the vote for candidates with that between the minority composition of the precincts and the vote. Reliable party identification measures are not usually available for precincts in past elections, however. In the recent applications, the measure of party identification has been based on the votes cast for the candidates of the political parties in a previous election. If the correlation between party, as measured, and the vote tends to be higher than that between the minority composition and the vote, it is argued that party is the more important determinant of the vote and therefore that voting is not racially polarized.

Another common approach to minimizing the impact of the plaintiffs’ evidence of racial divisions is to include in the analysis elections in which there are no minority candidates. These are almost always white-on-white elections, in terms of candidates, and the estimated divisions in the vote are derived through the same measurement techniques that the plaintiffs employ. Without a biracial choice of candidates, racial differences in candidate preferences will usually appear less often. Even when the preferences are split, the divisions are typically not as intense as in biracial elections, which may result in the white candidates preferred by minority voters in these elections winning. Despite the evidence of racial divisions varying greatly between the two types of elections, the defendants’ experts treat all elections as equally probative. Given that the white-on-white elections are typically much more numerous than biracial elections in challenged jurisdictions, the findings for these elections dilute the evidence from the biracial contests, leading to the conclusion that voting is not polarized or, if it is, that minority votes are not diluted because the candidates preferred by minority voters win a sufficient number of elections.

2.11.3.2.6.2 Data scaling and aggregation issues

Another important consideration in vulnerability assessments is the fact that spatial data can be aggregated to provide a more generalized representation of an area, but in the absence of additional information, data cannot be scaled down to finer levels. This is an example of the ecological fallacy: individual attributes cannot be deduced from statistical inferences of the group to which such individuals belong. Block groups may be too coarse for local government planning efforts (Garbutt et al., 2015). However, block groups cannot be easily downscaled due to uncertainty in how the individuals in the population and their characteristics are spatially distributed within each block group. This is a major issue when only a portion of a block group polygon intersects a hazard zone, as one cannot accurately discern the individuals and characteristics of the population within the given hazard zone (Berke et al., 2015; Sahin and Mohamed, 2013). In this case, part of the population of the block group is exposed to the hazard, but the data available assumes spatial homogeneity of socioeconomic characteristics.

When intersecting socioeconomic polygons with hazard exposure, we may assume that the population is evenly distributed across the polygon and that the total number of individuals (and their respective characteristics) exposed to the hazard is proportional to the percentage area of the socio-demographic polygon that is covered by the hazard exposure polygon. For example, in determining the number of residents in a floodplain, one would assume that the fraction of the population in the floodplain is equivalent to the fraction of the area in the floodplain. If 50% of the block group falls within the floodplain, then we should assume that 50% of the population is also in the floodplain and that demographic characteristics are uniform across the population. When assessing the vulnerability of Sarasota County, FL to elevated storm surge due to projected SLR, Frazier et al. (2014) used census blocks as their unit of analysis, determining the areal percentage of each block in the hazard zone and then including this percentage as a vulnerability indicator within their calculations.

Several researchers have developed techniques to better estimate the population at risk. Felsenstein and Lichter (2014) improve upon the simple areal approach by using building data. They calculate the total floor space per building and then proportionately allocate people and their socioeconomic characteristics to buildings on a per square meter basis. They then re-aggregate to the hazard area. This provides a more accurate spatial distribution of inhabitants and allows for a better estimate of population exposed to hazards, but it still assumes that demographic characteristics are uniform across the population.

Prasad (2016) addresses this challenge in a different way through the use of dasymetric mapping, a technique that utilizes ancillary data, such as land use and land cover data, to allocate the population based on density. To evaluate the evacuation needs of residents in the South East Florida floodplain, he created a 30 × 30 m raster grid population estimate based on land use and land cover data. Population was excluded from uninhabited areas (e.g., golf courses, agricultural land, water) and allocated to residential areas based on whether land cover analysis identified areas as high, medium, or low density. Then, he used the floodplain boundary as a mask to extract the pixels in the floodplain. This technique provides a more realistic estimate of the distribution of people within a given area and their vulnerability to the hazard of interest.

Berke et al. (2015) use a similar approach to Prasad (2016) in their assessment of the social vulnerability of Washington, NC. Using LandScan data, a global population distribution model developed at Oak Ridge National Laboratory that calculates the number of people living within 90-m cells, they applied a weighting system for social vulnerability indicators; densely populated cells with high social vulnerability were scored higher than sparsely populated cells with a similar social vulnerability (Berke et al., 2015). LandScan is commonly used to disaggregate population counts within administrative units, transforming data on the census-tract level to a smaller, finer scale grid (Mondal and Tatem, 2012; Li et al., 2009). LandScan compiles data from population censuses around the world, distributing the population into cells based on land cover, proximity to roads, terrain slope, and nighttime light intensity (Mondal and Tatem, 2012). LandScan provides “ambient” population distributions, integrating diurnal movements and collective travel habits into a single measure. Global Rural Urban Mapping Project (GRUMP) is another product commonly used to estimate populations at risk of SLR and coastal hazards (Neumann et al., 2015; Mondal and Tatem, 2012). Similar to LandScan, GRUMP disaggregates population data from administrative units to grids using nighttime light satellite data. Nighttime light intensity is used as a proxy measure to identify urban areas. GRUMP distributes the population within the administrative unit based on rural–urban extents.

While disaggregated population datasets can improve estimates of vulnerable populations, globally it is important to recognize that different datasets may influence the accuracy of results. Mondal and Tatem (2012) highlight this issue by comparing estimates of population in low-lying coastal areas using LandScan and GRUMP. While these disaggregated datasets produce similar results for developed countries in Europe and North America, there were substantial differences in less-developed countries in Africa, Asia, and South America. Some of these countries do not conduct regular censuses of their populations, thus limiting overall knowledge of human population distributions. As models of biophysical change improve in accuracy and detail, knowledge of human population distribution, especially in less-developed regions of the world, may remain a major limiting factor in our understanding of vulnerability to particular hazards, especially for hazards that have distinct spatial extents (Mondal and Tatem, 2012).

Census Data

Census data are usually provided as values for census units that vary spatially in size, geometry, and orientation (Fig. 2B). This variation leads to the modifiable areal unit problem (MAUP). The main problem with such data is that since the support is not constant across space, it is not reasonable to compare values directly, and it is therefore not possible to apply classical statistical and geostatistical techniques directly to such data without modification. Why is this so? From Eq. (10), it can be seen that variation is a function of the support: larger supports lead to less variance (smoother variation) and vice versa. In census data, in which the supports vary hugely from place to place, comparison between data is problematic. The MAUP is often said to comprise two main components: the aggregation and zonation problems.

The Ecological Fallacy Controversy

On the face of it, case definition would seem bound by some basic rules. Organizations should not be compared to people, or people to administrative governmental units. This approach posits multiple “levels of analysis” and holds that comparison must treat cases on the same level—persons with persons, organizations with organizations, and so forth. This standard of comparison is necessary, it has been argued, to avoid the “ecological fallacy,” an example of which would include inferring relationships between attributes of individuals (income and political conservatism) on the basis of aggregate relationships between those same attributes found in more encompassing units (such as provinces). Recently, efforts to come to terms with the problem have yielded some fruitful procedures of ecological regression, even if the precept of avoiding inferences across levels remains a useful initial rule of thumb.

Yet there are two further issues. First, certain considerations may call for a different methodological strategy than one that defines analysis in relation to “levels.” Put simply, there is no epistemological guarantee that studying cases at a given level of analysis captures the relevant social processes in a given social phenomenon. Second, as Georg Simmel pointed out long ago, a given social form (e.g., conflict) can manifest at quite different scales and within different structures of social organization. These two points imply, respectively, that comparisons may analyze cases defined as wholes that transcend levels, and that cases at radically different levels of analysis may be compared, providing there is a good theoretical rationale for doing so. Indeed, this possibility has been explicitly theorized by Charles Tilly.

3 Human Ecology’s General Theoretical Contribution to Macrolevel Demography

It is clear that human ecology has contributed substantially to the preservation and advance of macrolevel theory in the social and behavioral sciences, generally, and in demography, in particular (Poston and Frisbie 1998). However, in the mid-twentieth century, two events combined to diminish the interest of demographers and other social scientists in macro-level analysis. The first was the publication of work dealing with what came to be known (erroneously) as the ‘ecological fallacy.’ Robinson (1950) argued that results of research in which aggregates are the units of analysis cannot be used to infer relationships among individuals and that a large proportion of research that employs aggregate data does so only because information on individuals is not available. The second was actually a sequence of events involving the emergence of modern techniques of sampling and survey analysis which greatly enhanced the opportunity for rigorous microlevel studies (Linz 1969). For a time, demography listed far toward reliance on individual-level research, even in the face of warnings by renowned scholars that the discipline was ill-served by a fixation at the microlevel (e.g., Ryder 1980).

A more balanced view prevails, partially due to the efforts of ‘ecological demographers’ both early on (Schnore 1961) and later (Namboodiri 1988). As it turned out, Robinson’s thesis was only partially correct. The problem identified by Robinson is not ‘ecological’ in nature, but rather an issue that arises whenever cross-level generalizations of any kind are contemplated. Moreover, many of the central tenets of human ecology are inherently macrolevel constructs devoid of any counterpart at the individual level. For example, the concept of the division of labor makes sense only when applied to groups. Analogous reasoning applies to many demographic variables. Individuals are born, they die, and in between they may migrate, but only groups, not individuals, have birth, mortality or migration rates.

A signal contribution of human ecology has thus been the development of a theoretical framework for a wide range of demographic studies of organized aggregates. Examples include investigations of the relationship between commodity exchange and position of cities in the US metropolitan hierarchy (Eberstein and Frisbie 1982), as well as in the worldwide system of cities (Meyer 1986), the effects on the volume and rate of migration, of functional niche and extent of the division of labor (Murdock et al. 1992, Poston and Mao 1996), changes in the social stratification of suburbs (Guest 1978, Krivo and Frisbie 1982), segregation of racial and ethnic populations (Massey and Denton 1989), and the ‘birth’ and ‘death’ rates of formal organizations (Carroll 1984, Hannan and Freeman 1977). Such work, in turn, offers a substantive grounding for mutlilevel analyses, in which, e.g., the behavior of individuals is partially explained in terms of the social or ecological context in which they exist.

Solutions to the Ecological Inference Problem?

A second basic approach, described in a 1953 study by Duncan and Davis, is based on establishing bounds for the minimum and maximum possible for each cell of a cross-tabulation in each of the aggregate units. By summing these extrema up over the data set, it is possible to determine with 100% confidence the minimum and maximum bounds of the correlation that could obtain in the individual-level data.

In 1997, King proposed a “solution” to the ecological inference (EI) problem, the EI technique. It was also developed in the context of dichotomous dependent variables. The EI technique combines the method of bounds with the Goodman regression technique, and estimates the system using maximum likelihood and numerical simulation, assuming a bivariate normal distribution for the parameters. Critics, however, have pointed out a number of flaws with King’s technique, a review of which is beyond the scope of this essay. Important critiques were done by Anselin in 2000, Anselin and Cho in 2002, Freedman in 1998, and McCue in 2001.

In other words, the narrow focus of King’s technique is reconstructing a description of the individual data, not evaluating a causal model. This is an adequate goal in King’s motivating example, ascertaining voting patterns by race for the purpose of redistricting litigation. But in virtually any other social science application, our interest is in a causal model that cannot be reduced to a contingency table. Even in voting analysis, there are substantively interesting questions about whether racial identity affects voting net of other factors, such as income, occupation, and so on. Further, King readily acknowledges that his method will be less effective when the dependent variable is continuous, because no information is gleaned from bounds. These are rather important limitations.

Further discussions of approaches to reduce bias in ecological inference were provided by Achen and Shively in 1995, Cho in 2001, and Freedman in 1991 and 2002.

2 The Impact of the Ecological Fallacy on Research Practices

Although the term ecological fallacy is most often associated with W. S. Robinson, Robinson does not use the term in his classic 1950 article. Instead he uses the term ‘ecological correlation,’ and he states that his analysis ‘provides a definite answer as to whether ecological correlations can validly be used as substitutes for individual correlations. They cannot’ (Robinson 1950, p. 357). Robinson uses illiteracy data from the 1930 US census to show the discrepancy between ecological correlations and individual correlations. The correlation between percent black and percent illiterate is r=0.77 across States and r=0.95 across nine larger geographic divisions of the USA. The size of those ecological correlations stands in stark contrast to the size of the individual-level relationship between race (black vs. others) and illiteracy (r=0.20). As a second example, Robinson notes that the ecological correlation of percent foreign-born and percent illiterate across States is large and negative (r=−0.53), suggesting that the foreign-born are substantially less likely to be illiterate. Yet the foreign-born actually are more likely to be illiterate, as shown by the positive correlation at the individual level (r=0.12).

Whereas Robinson focused on the danger of using aggregate data to draw conclusions about the behavior of individual people, the ecological fallacy problem in fact applies to inferences across levels of aggregation in general. Individuals need not be people. The terms individual level and aggregate level as used here refer to relative levels of aggregation. To illustrate, the term ‘individual’ could refer to a single church congregation within a population of congregations. The ecological fallacy problem would arise if a researcher tried to use data on racial diversity and attendance growth rates across church denominations (collections of congregations) to draw conclusions about the effect of racial diversity on local church growth. Because parishioners attend a local congregation, it is racial diversity at the local level, not at the denomination level, that is the natural focus here. One could of course survey local congregations in this instance, but the survey would ask questions about a collective (a congregation) rather than about a person.

It would be difficult to overstate the impact Robinson’s article has had on social science research during the second half of the twentieth century. The use of ecological correlations to study individual-level relationships had been commonplace before Robinson’s article, and the article sharply curtailed that practice. The article also served to motivate the development of survey research. If aggregate data are not adequate to study individuals, then social scientists need data on individuals. One efficient way to gather data on individuals is to ask them questions. So in this way Robinson’s message about the need for individual-level data to study individuals no doubt played a role in the amassing of the large survey data sets that have become standard fare in social science research in the twenty-first century.

It is sometimes difficult or impossible to collect survey data to overcome the ecological fallacy problem, however, for two main reasons. First, individuals might be hard to reach. The extreme case of this occurs in historical research, where the pertinent individuals are dead. For this reason, historical research is especially plagued by the ecological fallacy problem (geography is another discipline especially affected, since geographic research is often based on spatial units). Aggregate data often are the only data available to historians, and it is not possible to go back in time to collect data to determine who voted for the Nazis, for example. Second, individuals might be reachable, but the needed information is sensitive. To protect the privacy of individuals, government agencies in some instances aggregate individual-level data before releasing the data to researchers (see Aggregation: Methodology). But aggregation in turn creates the risk that researchers using the aggregate data might commit the ecological fallacy.

The Ecological Fallacy

In 1950, Robinson coined the term ecological fallacy to refer to the error of interpreting variations in environmental settings as variations among individuals. One tactic for solving Robinson’s ecological fallacy is to construct surveys in which questions clearly state whether they are asking personal opinions of the subject or general assessments of an environment setting. A Likert scale example of an ecological (i.e., environmental) question is to ask respondents to agree or disagree with the comment, “Sometimes class is very disorganized.” A comparable example in which the individual is the unit of analysis is to ask respondents to agree or disagree with the comment, “Sometimes I am not prepared when I come to class.” The ecological question provides a generalized assessment of the environment without targeting the source of disorganization. In the ecological example, it is unclear as to what unit of analysis the subjects are responding to—the setting, the teacher, the other students, themselves, or all of these.

Richards and colleagues compared the use of individualist and ecological units to analyze classroom environments. They used the Classroom Environment Scales developed by Moos and Trickett, which consist of true–false questions about the classroom environment. Richards et al. (1991) noted that the questions were “modeled on and resemble the type of questions used in objective personality tests” (p. 425). Consequently, measures of dispersion (such as standard deviation) were much higher among individuals in settings than across settings and reliability measures (alpha) were also higher across than within settings. Richards et al. also suggested that assessments of setting measures were mediated by personality differences between the individuals and that this confounded the results within any one setting. Thus, survey questions should be crafted so that they distinguish and elicit assessments of the environmental setting rather than serve as “disguised measures of individual differences.”

Richards and colleagues use the terms ecology and settings interchangeably. However, it should be remembered that, strictly speaking, the setting is not the unit of analysis but the group that inhabits the setting. The actual classroom does not fill out a questionnaire, students do. The Richards et al. study is important because it unequivocally confirms that by themselves, and without a theoretical justification, individuals as the unit of analysis are invalid and unreliable units by which to measure setting-level characteristics. It should be noted that by “setting,” Richards et al. are referring to the small-scale groups that inhabit the setting and thus setting is a group-level unit. If the goal of the study is to understand the characteristics and dynamics of settings (in this case, the classroom), then the proper sample for the study is settings and not individuals, and the goal of the researcher is to examine variation between settings and not between individuals.

In 1997, Gary King proposed a statistical solution to the ecological inference problem. Leo Goodman had previously proposed an ecological regression model to estimate individual differences from census data. King added to Goodman’s model by using random coefficients to further minimize the aggregation bias. His solution has met with partial success in finding estimators of subpopulations within a larger population. However, although statistical sampling is a powerful tool, statistics is not good at low-level inferences—that is, reducing the whole to its components, a kind of reverse statistics.

The ecological fallacy is the error of attributing the characteristics of a population to an individual. Statistical inference is intended to generalize from a sample population to the whole population. The goal of statistics is to generalize from the particular to the whole and not from the whole to the particular. As such, statistics cannot offer a solution to the ecological fallacy. Data on individuals or on subpopulations within a larger population can best be obtained by ensuring that the unit of analysis is the individual or the subpopulation and not the larger population. As Richards and colleagues note, this problem can be avoided by designing survey instruments that elicit individual characteristics and attitudes. It is only from individualistic data that the researcher can track individual and subpopulation characteristics when necessary.

In a study in which local and individual hospitalization rates were derived from community-level estimates of various indicators of socioeconomic status (SES), Hofer noted that SES community profiles may not be representative of those individuals in the community who are actually going to the hospital. For example, it is known that the proportion of elderly who have medical coverage is far greater than it is for young adults, and that some of these elderly patients will use the hospital many times. To obtain accurate estimates of the subpopulations using and not using the hospital, it is necessary to obtain data on samples of individuals, not social aggregates. The best aggregate estimator of subpopulation or individual differences is to either ensure that the individual characteristics to be analyzed are representative of the aggregate or to use complete analytical models that target only that set of SES data pertinent to a target population. In their study on hospitalization rates, Billings et al. found it necessary to include age and income interactions in assessing SES variables in small area studies.

Although ecological (groups) units comprise individuals, their characteristics are not equivalent to those of the individuals in the group; therefore, one has to apply a different theory to studies that use collectivities as units of analysis than to studies that use the individual as the unit of analysis. When collectivities are the units of analysis, the proper subject of inquiry should be the overall characteristics and emergent properties of populations. Group-level characteristics may be very different from those of the individual members of the group. Ethnographic and psychological studies are frequently guilty of the opposite of the ecological fallacy: the fallacy of mapping individual characteristics onto a group. This problem, called the “individual differences fallacy” by Richards in 1990, is discussed next.

1.22.2.3 Spatial Extent: Continuous Surfaces and Raster Scale

Perhaps the disciplines that have addressed the problems of ecological fallacy related to geospatial data most directly have been ecology, natural resources, and remote sensing. Considerable research in these fields grapples with the particular issue of scale and scaling as it relates to the ability to use spatial data to link spatial patterns with natural processes (Blöschl, 1996; Hunsaker et al., 2013; Lowell and Jaton, 2000; Mowrer and Congalton, 2003; Quattrochi and Goodchild, 1997; Sui, 2009; Wu et al., 2006). Landscape processes do not always operate on the scales represented in geospatial data, yet the geospatial data we use in a GIS to assess these systems imposes a fixed scale within which we attempt to understand them. Especially in disciplines related to ecology and natural resources, spatial data analyses revolve around use of the raster data structure to represent continuous surfaces. The issue of spatial extent is exemplified by the grid cell structure and the scale it imposes on spatial analyses.

Placement of discrete boundaries impacts analyses and contributes uncertainty associated with derived results. This is considerable when using the raster data structure. Although rasters represent continuous surfaces, the grid cell structure itself imposes a discrete boundary and associated scale of representation. In the raster data structure, the spatial support or resolution of spatial datasets is predefined, determined by mechanisms of the satellite (in the case of remotely sensed imagery) or grid cell resolution (in the case of digital elevation models (DEMs)), without consideration of the natural processes that are evaluated using these data (Dark and Bram, 2007).

Continuous surfaces represent spatial features that are not discrete and commonly represented in a GIS using uniform grids. This raster grid cell resolution imposes a measurement scale on the nature of geospatial analyses and, by association, a scale on the process (e.g., hydrologic, ecologic) these data and associated analyses represent. The concept of resolution is closely related to scale and refers to the smallest distinguishable component of an object (Lam and Quattrochi, 1992; Tobler, 1988). The grid cell is also referred to as the spatial support, a concept in geostatistics referring to the area over which a variable is measured or predicted (Dungan, 2002). Spatial resolution is related to the sampling interval. The Nyquist sampling theory states that the sampling rate must be twice as fine as the feature to be detected. The sensitivity of model input parameters and model predictions to spatial support have been documented in numerous geospatial analyses and remains an important factor in our understanding, assessment, and quantification of uncertainty in spatial data and related modeling applications (Wechsler, 2007).

Practitioners often do not have control of the grid cell resolution of a dataset (e.g., products provided from satellite remote sensing or government-produced DEMs). Subgrid variability—that is variability at scales larger than those captured by the grid cell area—cannot be resolved or captured using a typical raster grid cell structure. This is changing as new technologies place the decision for selecting an appropriate support in the hand of the practitioners, such as data derived from UAV platforms.

As technologies advance, new spatial datasets are continually being developed. In recent years, the commercial availability of low-cost hardware and embedded computer systems has led to an explosion of lightweight aerial platforms frequently referred to as unpiloted aerial vehicles (UAVs) or “drones”. UAVs are becoming a powerful cost-effective platform for collection of remotely sensed images. Advances in computer vision software have enabled the construction of 3D Digital Surface Models (DSMs) from acquired imagery using Structure from Motion (SfM). SfM uses complex computer algorithms to find matching points from overlapping images, enabling reconstructions of surface feature reconstructions from overlapping 2D images (Fonstad et al., 2013; Westoby et al., 2012).

UAV-derived imagery and surfaces are cost effective, accessible, and facilitate data collection at spatial and temporal scales previously inaccessible. As such, they are becoming widely used data sources in a wide range of disciplines and applications including geomorphological mapping (Gallik and Bolesova, 2016; Hugenholtz et al., 2013), vegetation mapping (Cruzan et al., 2016), and coastal monitoring (Goncalves and Henriques, 2015). Point clouds obtained from SfM-derived surfaces are used to generate digital surface models (DSMs).

Data quality is addressed using RMSE to quantify the accuracy of UAV-derived surfaces and vertical accuracies in the centimeter range are commonplace (Harwin and Lucieer, 2012; Neitzel and Klonowski, 2011; Reshetyuk and Martensson, 2016; Verhoeven et al., 2012). However, statements of accuracy and data quality are no substitute for estimates of uncertainty and resulting decisions for fitness-of-use. Data quality and accuracy assessment have become mainstream practice. The challenge remains to bridge the gap between representation of data quality and mechanisms for quantifying and communicating uncertainty.

There is a long tradition, in the social and life sciences, of attempts to infer individual behavior from group behavior. Durkheim’s book on suicide is an early example. The ‘ecological fallacy’ consists of ascribing to individuals the characteristics of groups to which they belong, even though the relevant individuals may not share such characteristics. The issues are discussed in seminal papers by Robinson, Duncan and Davis, and Goodman, which are summarized here. Ecological regression is considered, along with recent work on random-coefficients models. Examples are drawn from epidemiology, voting rights, and survey data.

The Defendants’ Response

The defendants’ response to the plaintiffs’ evidence takes several forms. One is to argue that precinct-level data are not a valid basis for deriving the estimates reported. This often entails little more than a recitation of the ecological fallacy, which in this context states that we cannot draw inferences about the distributions of candidate preferences of the individuals within groups from data based on heterogeneous aggregations (precincts) of these groups. This response is rarely successful, however, in light of the pronounced differences usually observed across these aggregates.

A far more frequent response is to offer a different definition of what racially polarized voting entails, a definition under which such divisions are, by themselves, treated as irrelevant. Defendants often argue that if voting is to be considered polarized, it must be based on racial animus. Voting, in short, must be more than racially divided; it must also be racially motivated. Under this definition, group divisions in candidate preferences, no matter how acute or consistent, are not sufficient to establish polarized voting. Rather, additional evidence showing that these preferences were motivated by racial animus is required. This necessary condition, given this definition, is normally introduced by the testimony of an expert. At times, the jurisdictions simply argue that the burden of proving that racism is the causal factor, or at least a pronounced causal factor, rests with the plaintiffs. Experts called by defendants testify that the plaintiffs’ evidence of group divisions, no matter how pronounced and persistent the divisions may be, is simply descriptive and establishes at best correlation not causation. Without evidence of racial motivations behind the racial divisions, defendants argue, the plaintiffs must lose.

Racial divisions in voting patterns could be viewed, however, as establishing a reasonable presumption of polarized voting, even if racial animus is a definitional criterion. If this is the case, then a defendant jurisdiction must rebut this presumption through evidence of its own that shows the absence of racial animus. This requires that the defendants themselves provide evidence that demonstrates nonracial explanations for the divisions. This approach involves identifying variables other than the relative presence of a minority group’s voters across the precincts that might relate to the voters’ choices. Variables suggested to have this explanatory power include the party identifications of the voters, their incomes, the issues that concern them, and the geographical distance between the residences of candidates and the precincts within which voters reside—variables that themselves typically relate to the racial composition of the precincts.

These actual multivariate analyses deviate from the precinct-based analyses used to demonstrate racial divisions. Although some of the suggested variables can be directly measured at the precinct level for past elections, others such as the party identifications and issue concerns of voters cannot. The actual analysis therefore shifts to an examination, across elections, of the characteristics of candidates and their campaigns. The unit of analysis becomes elections, not precincts. Variables such as the party affiliation of the candidates (rather than the voters), their incumbency status, their name identification, the relative cost of their campaigns, and the race of the candidates are related to the outcomes of elections, measured by the overall percentage of the votes the various candidates received or simply whether the candidates won or lost. These analyses do not reveal whether or not the voters are divided along racial lines but, rather, whether the race of the candidate has a separate, independent effect on the outcome measures when the other variables are included. If it does not, it is argued, the divisions in candidate preference are cleansed of any racial content.

Another approach to the nonracial explanation argument has been employed recently. This approach does rely on the precinct as the unit of analysis. It involves attempting to measure the party identification of the voters in past elections at the precinct level and then comparing the bivariate correlation coefficient between that variable and the vote for candidates with that between the minority composition of the precincts and the vote. Reliable party identification measures are not usually available for precincts in past elections, however. In the recent applications, the measure of party identification has been based on the votes cast for the candidates of the political parties in a previous election. If the correlation between party, as measured, and the vote tends to be higher than that between the minority composition and the vote, it is argued that party is the more important determinant of the vote and therefore that voting is not racially polarized.

Another common approach to minimizing the impact of the plaintiffs’ evidence of racial divisions is to include in the analysis elections in which there are no minority candidates. These are almost always white-on-white elections, in terms of candidates, and the estimated divisions in the vote are derived through the same measurement techniques that the plaintiffs employ. Without a biracial choice of candidates, racial differences in candidate preferences will usually appear less often. Even when the preferences are split, the divisions are typically not as intense as in biracial elections, which may result in the white candidates preferred by minority voters in these elections winning. Despite the evidence of racial divisions varying greatly between the two types of elections, the defendants’ experts treat all elections as equally probative. Given that the white-on-white elections are typically much more numerous than biracial elections in challenged jurisdictions, the findings for these elections dilute the evidence from the biracial contests, leading to the conclusion that voting is not polarized or, if it is, that minority votes are not diluted because the candidates preferred by minority voters win a sufficient number of elections.

2.11.3.2.6.2 Data scaling and aggregation issues

Another important consideration in vulnerability assessments is the fact that spatial data can be aggregated to provide a more generalized representation of an area, but in the absence of additional information, data cannot be scaled down to finer levels. This is an example of the ecological fallacy: individual attributes cannot be deduced from statistical inferences of the group to which such individuals belong. Block groups may be too coarse for local government planning efforts (Garbutt et al., 2015). However, block groups cannot be easily downscaled due to uncertainty in how the individuals in the population and their characteristics are spatially distributed within each block group. This is a major issue when only a portion of a block group polygon intersects a hazard zone, as one cannot accurately discern the individuals and characteristics of the population within the given hazard zone (Berke et al., 2015; Sahin and Mohamed, 2013). In this case, part of the population of the block group is exposed to the hazard, but the data available assumes spatial homogeneity of socioeconomic characteristics.

When intersecting socioeconomic polygons with hazard exposure, we may assume that the population is evenly distributed across the polygon and that the total number of individuals (and their respective characteristics) exposed to the hazard is proportional to the percentage area of the socio-demographic polygon that is covered by the hazard exposure polygon. For example, in determining the number of residents in a floodplain, one would assume that the fraction of the population in the floodplain is equivalent to the fraction of the area in the floodplain. If 50% of the block group falls within the floodplain, then we should assume that 50% of the population is also in the floodplain and that demographic characteristics are uniform across the population. When assessing the vulnerability of Sarasota County, FL to elevated storm surge due to projected SLR, Frazier et al. (2014) used census blocks as their unit of analysis, determining the areal percentage of each block in the hazard zone and then including this percentage as a vulnerability indicator within their calculations.

Several researchers have developed techniques to better estimate the population at risk. Felsenstein and Lichter (2014) improve upon the simple areal approach by using building data. They calculate the total floor space per building and then proportionately allocate people and their socioeconomic characteristics to buildings on a per square meter basis. They then re-aggregate to the hazard area. This provides a more accurate spatial distribution of inhabitants and allows for a better estimate of population exposed to hazards, but it still assumes that demographic characteristics are uniform across the population.

Prasad (2016) addresses this challenge in a different way through the use of dasymetric mapping, a technique that utilizes ancillary data, such as land use and land cover data, to allocate the population based on density. To evaluate the evacuation needs of residents in the South East Florida floodplain, he created a 30 × 30 m raster grid population estimate based on land use and land cover data. Population was excluded from uninhabited areas (e.g., golf courses, agricultural land, water) and allocated to residential areas based on whether land cover analysis identified areas as high, medium, or low density. Then, he used the floodplain boundary as a mask to extract the pixels in the floodplain. This technique provides a more realistic estimate of the distribution of people within a given area and their vulnerability to the hazard of interest.

Berke et al. (2015) use a similar approach to Prasad (2016) in their assessment of the social vulnerability of Washington, NC. Using LandScan data, a global population distribution model developed at Oak Ridge National Laboratory that calculates the number of people living within 90-m cells, they applied a weighting system for social vulnerability indicators; densely populated cells with high social vulnerability were scored higher than sparsely populated cells with a similar social vulnerability (Berke et al., 2015). LandScan is commonly used to disaggregate population counts within administrative units, transforming data on the census-tract level to a smaller, finer scale grid (Mondal and Tatem, 2012; Li et al., 2009). LandScan compiles data from population censuses around the world, distributing the population into cells based on land cover, proximity to roads, terrain slope, and nighttime light intensity (Mondal and Tatem, 2012). LandScan provides “ambient” population distributions, integrating diurnal movements and collective travel habits into a single measure. Global Rural Urban Mapping Project (GRUMP) is another product commonly used to estimate populations at risk of SLR and coastal hazards (Neumann et al., 2015; Mondal and Tatem, 2012). Similar to LandScan, GRUMP disaggregates population data from administrative units to grids using nighttime light satellite data. Nighttime light intensity is used as a proxy measure to identify urban areas. GRUMP distributes the population within the administrative unit based on rural–urban extents.

While disaggregated population datasets can improve estimates of vulnerable populations, globally it is important to recognize that different datasets may influence the accuracy of results. Mondal and Tatem (2012) highlight this issue by comparing estimates of population in low-lying coastal areas using LandScan and GRUMP. While these disaggregated datasets produce similar results for developed countries in Europe and North America, there were substantial differences in less-developed countries in Africa, Asia, and South America. Some of these countries do not conduct regular censuses of their populations, thus limiting overall knowledge of human population distributions. As models of biophysical change improve in accuracy and detail, knowledge of human population distribution, especially in less-developed regions of the world, may remain a major limiting factor in our understanding of vulnerability to particular hazards, especially for hazards that have distinct spatial extents (Mondal and Tatem, 2012).

Census Data

Census data are usually provided as values for census units that vary spatially in size, geometry, and orientation (Fig. 2B). This variation leads to the modifiable areal unit problem (MAUP). The main problem with such data is that since the support is not constant across space, it is not reasonable to compare values directly, and it is therefore not possible to apply classical statistical and geostatistical techniques directly to such data without modification. Why is this so? From Eq. (10), it can be seen that variation is a function of the support: larger supports lead to less variance (smoother variation) and vice versa. In census data, in which the supports vary hugely from place to place, comparison between data is problematic. The MAUP is often said to comprise two main components: the aggregation and zonation problems.

The Ecological Fallacy Controversy

On the face of it, case definition would seem bound by some basic rules. Organizations should not be compared to people, or people to administrative governmental units. This approach posits multiple “levels of analysis” and holds that comparison must treat cases on the same level—persons with persons, organizations with organizations, and so forth. This standard of comparison is necessary, it has been argued, to avoid the “ecological fallacy,” an example of which would include inferring relationships between attributes of individuals (income and political conservatism) on the basis of aggregate relationships between those same attributes found in more encompassing units (such as provinces). Recently, efforts to come to terms with the problem have yielded some fruitful procedures of ecological regression, even if the precept of avoiding inferences across levels remains a useful initial rule of thumb.

Yet there are two further issues. First, certain considerations may call for a different methodological strategy than one that defines analysis in relation to “levels.” Put simply, there is no epistemological guarantee that studying cases at a given level of analysis captures the relevant social processes in a given social phenomenon. Second, as Georg Simmel pointed out long ago, a given social form (e.g., conflict) can manifest at quite different scales and within different structures of social organization. These two points imply, respectively, that comparisons may analyze cases defined as wholes that transcend levels, and that cases at radically different levels of analysis may be compared, providing there is a good theoretical rationale for doing so. Indeed, this possibility has been explicitly theorized by Charles Tilly.

3 Human Ecology’s General Theoretical Contribution to Macrolevel Demography

It is clear that human ecology has contributed substantially to the preservation and advance of macrolevel theory in the social and behavioral sciences, generally, and in demography, in particular (Poston and Frisbie 1998). However, in the mid-twentieth century, two events combined to diminish the interest of demographers and other social scientists in macro-level analysis. The first was the publication of work dealing with what came to be known (erroneously) as the ‘ecological fallacy.’ Robinson (1950) argued that results of research in which aggregates are the units of analysis cannot be used to infer relationships among individuals and that a large proportion of research that employs aggregate data does so only because information on individuals is not available. The second was actually a sequence of events involving the emergence of modern techniques of sampling and survey analysis which greatly enhanced the opportunity for rigorous microlevel studies (Linz 1969). For a time, demography listed far toward reliance on individual-level research, even in the face of warnings by renowned scholars that the discipline was ill-served by a fixation at the microlevel (e.g., Ryder 1980).

A more balanced view prevails, partially due to the efforts of ‘ecological demographers’ both early on (Schnore 1961) and later (Namboodiri 1988). As it turned out, Robinson’s thesis was only partially correct. The problem identified by Robinson is not ‘ecological’ in nature, but rather an issue that arises whenever cross-level generalizations of any kind are contemplated. Moreover, many of the central tenets of human ecology are inherently macrolevel constructs devoid of any counterpart at the individual level. For example, the concept of the division of labor makes sense only when applied to groups. Analogous reasoning applies to many demographic variables. Individuals are born, they die, and in between they may migrate, but only groups, not individuals, have birth, mortality or migration rates.

A signal contribution of human ecology has thus been the development of a theoretical framework for a wide range of demographic studies of organized aggregates. Examples include investigations of the relationship between commodity exchange and position of cities in the US metropolitan hierarchy (Eberstein and Frisbie 1982), as well as in the worldwide system of cities (Meyer 1986), the effects on the volume and rate of migration, of functional niche and extent of the division of labor (Murdock et al. 1992, Poston and Mao 1996), changes in the social stratification of suburbs (Guest 1978, Krivo and Frisbie 1982), segregation of racial and ethnic populations (Massey and Denton 1989), and the ‘birth’ and ‘death’ rates of formal organizations (Carroll 1984, Hannan and Freeman 1977). Such work, in turn, offers a substantive grounding for mutlilevel analyses, in which, e.g., the behavior of individuals is partially explained in terms of the social or ecological context in which they exist.