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Papers of the Applied Geography Conferences (2008) 31: 195-205

APPLICATION OF SERIATION TO RELATIVE URBAN HOUSING QUALITY CLASSIFICATION IN ECUADOR AND BOLIVIA Betty E. Smith Department of Geology and Geography Eastern Illinois University Charleston, Illinois 61920 1. INTRODUCTION Benefits of nominal categorical data are greater freedom of expression of cultural, socioeconomic, and institutional context. A heuristic technique, seriation is used to reveal and classify data structure graphically. Seriation involves placing objects or observations in an order based on their attribute similarities. The more attributes shared, the closer the observations are in the ordering; likewise, the fewer attributes shared the more distant. Archaeologists seriate characteristics of artifacts to identify propinquity of attributes and infer chronology (O’Brien and Lyman, 1999). Geographers rarely seriate geographically referenced nominal data in spite of advances in computing and binary visualization capabilities. The objective of this research was to identify residential socioeconomic configuration of three South American cities by applying seriation to nominal census data. A relative housing quality index was developed as an indicator of poor, middle class, and elite neighborhoods. Part of a larger project to identify generalities about density structure of South American cities, the seriation of nominal housing data can provide a surrogate for income data not available. The three research sites varied in size and context. Medium size cities, Riobamba and Ibarra were tenth and fourteenth in the urban hierarchy of Ecuador with populations of 100,710 and 87,834 (INEC, 1992b, 1992a), respectively. At an elevation of 9,000 feet in the shadow of Chimborazo volcano, Riobamba grew from a population of 100,710 in 1990 to a population of 124,478 in 2001. Situated at 7800 feet elevation on gentle slopes of Imbabura volcano, the medium size city, Ibarra, grew over the same period from 87,834 to 108,666. Santa Cruz is the second largest city in Bolivia and quadrupled between 1970 and 1990, to approximately 600,000. Built on the subtropical plains east of the Andes, Santa Cruz Department has continued to grow. According to the World Gazetteer (Helders, 2008), the official 1992 Bolivian census put department population at 1,364,389 and the 2001 population was 2,033,739; estimated 2007 population was 2,541,151. 2. BACKGROUND Statistical techniques available to urban geographers often assume availability of normally distributed high level ratio type data, when in reality much data is low order nominal (e.g., house construction materials, type of water service available) (Wrigley 1985). The seriation method is a graphic information processing technique that is useful to researchers confronted with categorically measured nominal variables. Seriation has been used by archaeologists for classification of pottery and other artifacts (Dunnell, 1986; Duff, 1996; Ortman, 2000; Hurt et al., 2001), population and culture change over time and space (Lipo et al., 1997; Lyman et al., 1998; Lyman and O’Brien, 2000), and linguistics (Mallory, 1976). “Seriation as a scaling technique produces a formal arrangement of units, the significance of which must be inferred. Arrangement per se is a statistical matter, while the inference of significance is archaeological method” (Dunnell, 1970). Dunnell explained that seriation has been in the literature for more than fifteen years; although geology-based stratigraphy can only

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be applied to a single site, seriation has the potential to be applied across several sites to establish chronology. Seriation offers a visual means of examining data structure by reorganizing and presenting as homogeneous a picture as possible. The technique merges researcher judgment with computer power, graphically processing and simplifying data. Advantages over cluster analysis or factor analysis are that: 1) data structure is visualized as a simple black and white image, 2) 100 percent of original information remains intact, and 3) geography of data is retained when rearranging categories to best reflect generalized data structure. Geography is retained because the method uses a matrix in which rows are areal units (observations) and columns are binarized nominal variables. This contrasts with cluster, factor, and principal component methods that rely upon a symmetrical matrix in which variables are correlated with each other without regard to geographic location. Seriation was first developed by anthropologist Petrie (1899) and subsequently used by archaeologists to establish chronology of archaeological sites and ancient tools (Hodson et al., 1970). It is well suited to urban geography, but has received little attention. French cartographer Bertin (1981) published examples of graphics as a tool for information processing and problem solving. However, matrix size and speed of manipulation of rows and columns were limited in a manual approach. According to Muller (1983), The purpose of the matrix manipulation is to find the permutations which unveil associations or oppositions between rows and columns that lead to an interpretation of the structural relationships between geographical entities and their spatial attributes.... The manual process ideally converges toward a solution where both similarities between consecutive rows and similarities between consecutive columns are optimized. Visually the pattern of black cells in the new matrix appears more regular. The objective is to bring together those rows and columns that are most similar. Resultant groupings of characteristics can be interpreted and mapped to show regional distribution. Membership of a geographic unit in a group is mutually exclusive. Seriation today is a semi-automated process that uses human judgment at certain junctures. Bertin (1981, 9) noted that “the most important stages—choice of questions and data, interpretation and decision making—can never be automated” (Bertin 1981, 9). A key characteristic of seriation, and probably a major reason for its lack of frequent application, is that the method cannot be completely automated. Muller (1983) was the first to discuss the feasibility of automated seriation and used the technique to display the regional classification of employment structure in Canada by province, using a small 9 x 11 matrix. Although the seriation procedure cannot be completely automated, Muller (1983) attempted to formalize the process of measuring difference between rows and columns, thereby minimizing visual perception bias of similarities and differences. A problem encountered in seriation automation is the magnitude of considering all possible combinations. Parallel processing or alternative algorithms are possible solutions; the latter were applied empirically in this research. 3. DATA The Ecuador census (INEC, 1992a, 1992b) enumerated persons based upon location at moment of the census: Sunday morning, 25 November 1990. Ibarra data contain 108,943 observations, of which 21,109 are housing and 87,834 are population. Riobamba data contain 125,620 observations; 24,910 are housing and 100,710 are population. A Santa Cruz regional development corporation, Corporación Regional de Desarrollo de Santa Cruz (CORDECRUZ) concluded a 1988 survey of migration, employment, and housing in Bolivian cities of Santa Cruz, Montero, and Villa Busch (CORDECRUZ, 1988). This survey was a stratified random sample including more than 3,000 homes and 14,000 persons, representing approximately a two percent sample. Santa Cruz data contained 2,481 housing observations and 10,782

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population observations. Lacking access to a recent population census in Bolivia at the time of this research, the stratified random sample was used. To proceed with spatial analysis of housing, observations were aggregated to create new geographically referenced data. The 113 census areal units in Santa Cruz are called zonas, more or less equivalent to census tracts. Ibarra contained 144 sectores, also approximating census tracts, and Riobamba, 178 sectores. The zonas and sectores were digitized from original paper maps to form digital polygon coverage. Nominal data were sorted by sector and zona and tables were created showing percentage of each nominal classification. The predominant characteristic mode was selected as representative. Finally, a new dataset based on the modal values was merged with geographic coordinates derived from digitized maps. 4. METHODS Bjorke (1989) presented an alternative algorithm for automated seriation that reordered a two dimensional matrix of geographic areas (rows) and their qualitative characteristics (columns). This algorithm was revised and empirically tested by Bjorke and Smith (1996) and was used in this research to demonstrate reordering, classification, and comparison of relative housing quality. Census areal units are shown as rows and binarized categories of nominal variables are columns. As an example, if variable FLOOR has six possible categorical responses (wood, tile, brick, cement, earth, other), then FLOOR becomes six variables (FLOOR1, FLOOR2, etc.), each with a binary response of yes or no, one or zero, or a black or white pixel on a computer screen. Thus there are six columns for variable FLOOR. In a similar fashion, each category of each nominal variable is binarized, e.g., type of home, roof material, or availability of drinking water. The data matrix becomes considerably wider with a long list of variables. Binarizing categorical variables results in three matrices for the three study sites: 1) Ibarra has 144 rows and 53 columns, 2) Riobamba has 177 rows and 42 columns, and 3) Santa Cruz has 113 rows and 80 columns. On the computer screen each positive response is represented by a black pixel and each negative response by a white pixel. The original data matrix is represented by an image of scattered black and white pixels with no apparent organization. The objective is to rearrange the black pixels to achieve the highest possible degree of homogeneity, bringing as many black pixels together as possible without violating the integrity of any one row (census areal unit) or any one column (binarized categorical variable). The Bjorke (1989) algorithm for semi-automation of seriation is based upon minimization of entropy. Entropy is minimized when pattern is most ordered, most homogeneous. The approach of Bjorke and Smith (1996) expands the seriation criterion from minimum first order Hamming distance of a binary image to also include calculation of higher order neighbors. Hamming distance is the number of bits which differ between two binary strings. More formally, the distance between two strings A and B is ∑ | Ai - Bi |. Hamming distance is positively correlated with measure of entropy of an image and is therefore useful in defining seriation criteria. An image which has a high measure of entropy also has a high Hamming distance and likewise, an image which has a low measure of entropy has a low Hamming distance. However, Bjorke and Smith (1996) show the seriation criterion must evaluate not only nearest neighbors but all matrix rows. Although reordering of rows of black pixels may be automated, the decision regarding partitioning of the image into groups remains a judgment by the researcher. Thus, the solution is not deterministic. An issue with any classification scheme is selection of the number of groups. Appropriate generalization depends upon the problem to be solved, data structure, and researcher judgment. Since many descriptive urban land use models simply diagram distribution of poor, middle class, and elite socioeconomic groups, generalizing three broad groups of relative housing quality is quite useful. Cluster analysis can be a check for seriation results. Cluster analysis partitions a set of objects (observations) into homogeneous subsets

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based on inter-object similarities to develop subgroups that differ in meaningful ways. A VARCLUS (SAS, 1989) cluster analysis was conducted to compare group results for a maximum of three, four, seven, and eight clusters. Results of the cluster procedure confirmed the presence of the variables in the seriated groups, provided the variable was at least 90 percent present. An advantage of seriation is that a category of a single variable may be found in several real world groups and be represented in different proportions in the derived groups. In contrast to cluster analysis, seriation retains geography throughout analysis and each geographical areal unit is assigned to one and only one housing quality group which can then be mapped. 5. INTERPRETING THE SERIATED IMAGE OF IBARRA Ibarra graphic information images before and after seriation are shown in Figures 1 and 2. Each housing quality variable has been binarized; for example, ROOF with seven possible categorical responses (cement, asbestos, wood, zinc, tile, straw, other) became seven dichotomous variables in seven columns. For each geographic observation (census unit) one of the seven responses is the mode and that pixel is shaded black; the other six remain white. FIGURE 1 IBARRA BEFORE SERIATION

FIGURE 2 IBARRA AFTER SERIATION Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8

Both before and after seriation, graphic images contain some all black and all white columns. An all black column indicates all census tracts are predominantly characterized by this attribute, such as bottled gas for cooking in each of the cities. Other characteristics which appear as all black columns in some, but not all, of the three cities are separate room for kitchen, water pipe in home, public water, and electricity. Examples of all white columns are common shower, commercial enterprise in home, wood roofs, cane floors, well as a source of water, and river as a source of water. Uniform black or white columns provide the least information for classification purposes because they fail to differentiate. Characteristics of housing quality unique to a group offer the best information for defining that group. The following questions should be asked: 1) what variable category is unique to this group? and; 2) what variable category is lacking in this group but present in other groups? Seriation analysis (visual identification of pattern similarities) of binarized housing quality variables yielded eight groups. Groups in Figure 2 from top to bottom (separated by white lines) are Group 1 to Group 8. The eight groups were merged into three housing quality classifications for mapping and future spatial analysis (Table 1). To generalize three broad groups, Groups 1 and 2 form a unique part of the image, QUALITY 1. Groups 3, 4, 5, and 6 seem to fit together visually and were designated as

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TABLE 1 MERGING OF SERIATED GROUPS Ibarra, Ecuador QUALITY 1 = Group 1 Poor With Limited Urban Services + Group 2 In Town Poor QUALITY 2 = Group 3 All One-Bedroom + Group 4 In Town Better + Group 5 Room Rent + Group 6 Apartment Rent QUALITY 3 = Group 7 Good Quality Big Home + Group 8 Best Quality Riobamba, Ecuador QUALITY 1 = Group 1 Room Rent + Group 2 Metal Roof Owners + Group 3 Small Poor + Group 4 All One-Bedroom QUALITY 2 = Group 5 All Two Bedrooms + Group 6 Good Quality QUALITY 3 = Group 7 Best Quality Home Santa Cruz, Bolivia QUALITY 1 = Group 4 No Public Services Poor + Group 5 Earth Floor Poor QUALITY 2 = Group 2 Fair Services Small Home + Group 3 Poor Services Small Home + Group 6 Rural Room Rent + Group 7 All Rooms For Rent QUALITY 3 = Group 1 Best Quality Big Home

QUALITY 2, and Groups 7 and 8 form a third group, QUALITY 3. A number of all-black and all-white columns of pixels are evident in the Ibarra image: 100 percent of tracts have a predominant number of homes with a separate room for the kitchen and have bottled gas for cooking. None are predominantly homes containing commercial enterprise, or homes with wood roofs, cane floors, well water for water source, or river water for water source. Groups 1 and 2 are made up of poorer homes and were merged to form QUALITY 1, the lowest quality housing in Ibarra. Group 1 unique conditions (those conditions not present in other groups) are earth floor, non-public drains, water pipe outside of the lot, no electricity, water delivered by car, and no drains. Some tracts have no shower and lack public sewers. Although representation is fairly small, 10 to 30 percent, it is important because these housing characteristics are not present in the other seven groups. Group 1 consists of one bedroom detached homes with metal roofs, adobe walls, no electricity, and no telephone. All modal values represent owners, not renters. Lack of urban services, small size of homes and presence of earth floors and adobe walls suggest this group should be named POOR With Limited Urban Services. Each group member has a majority of homeowners. A check of geographic location of rows confirms that the sectors are located near Lake Yaguarcocha, north of city center and beyond city services. Group 2 also seems to be a poor housing quality group, but in contrast to Group 1, this group has city services. This is the only group in which no group members have a private bathroom. Indicators include all tracts with primarily one bedroom detached homes with metal roofs and brick or cement floors. Most modal values are adobe walls, water pipe in the house, and public drains. All tracts in this group have city services such as electricity, public water and trash pickup. Since these are small homes with adobe walls but with city services, the group was designated In-Town Poor. The next four sets of homes are of moderate quality and were merged to form QUALITY 2. Group 3 has no unique variables however it is the only group having no two room homes. Group characteristics are all one bedroom detached homes with brick or cement floors, electricity, public water, water pipe in the home, and nearly all sectors have trash pickup, public drains and one room homes. Eighty percent of sectors are predominantly owners. The group was named In-Town Small. Group 4 is the only group that consists of all sector modes of two room detached homes. All sectors consist of homes with electricity, public water, public drains, and water pipe in the home. Nearly all have private bathroom, private shower, and trash pickup. Again, the group is predominantly made up of owners.

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Presence of private bathrooms suggests better quality housing. This group is named In-Town Better. Group 5 has the unique characteristic of being the only group with sectors which primarily consist of rooms for rent, rather than detached homes. Not surprising, the group also consists of a high percentage (70 percent) renters. Sectors consist primarily of one room homes or one-bedroom homes. In contrast to other groups, nearly all homes have floorboards, suggesting second and third story dwellings. Combination of rooms for rent, one room homes and floorboards, suggest downtown location, perhaps residential rooms for rent located above first floor commercial uses. Nearly all floors in other groups are brick or cement. Availability of nearly all public services also suggests a downtown location, later confirmed by mapping. This group was named Room Rent. Group 6 is unique as the only group with some apartments and 100 percent renters. The group is served by nearly all city services and homes are slightly better quality than Group 5, indicated by presence in all cases of private bathrooms, private showers, cement and brick walls, cement roof and some larger two and three bedroom homes. Floor category is dominated by floorboards, suggesting as in Group 5, a second or third floor location or an older downtown residence, since newer dwellings have cement floors. This group was called Apartment Rent. The best quality homes are found in the last two groups and were merged to form QUALITY 3. Group 7 is the only group with some sectors dominated by dwellings with five rooms per home. More than half the sectors are predominantly three bedroom homes and all have private shower, private bathrooms, cement and brick walls, and cement roofs. All city services are available. Ninety percent are predominantly owners. Most homes have parquet floors, characteristic of recently built tract homes. This group was tagged as Good Quality Big Home. Group 8 is the only group that has no one bedroom homes. Homes are predominantly two and three bedroom homes which are all owner occupied. A high proportion of sectors have asphalt-composition roofs, an indication of better quality construction. A higher percentage of telephones are available than any other group. This group is called Best Quality. Of note, aggregation of population and housing data excluded institutions such as jails, hospitals, and boarding schools. 6. INTERPRETING THE SERIATED IMAGE OF RIOBAMBA Riobamba has more population than Ibarra and more census units. However, there are fewer columns and more categories with 100 percent representation for all groups, indicating Riobamba is a more homogeneous city in terms of housing quality. Figure 3 presents the Riobamba binarized housing data matrix before seriation. The seriated Figure 4 graphic suggests seven groups, although differentiation is less clear than Ibarra. FIGURE 3 RIOBAMBA BEFORE SERIATION

FIGURE 4 RIOBAMBA AFTER SERIATION Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7

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The Riobamba seriated image was most difficult of the three study sites to interpret because it lacked differentiating characteristics. At first glance, the image appears to fall into two very broad groups, the top four horizontal slices and the bottom three slices. However, closer examination suggests that each of seven groups may be identified as a unique part of the overall graphic. Best characteristics for interpretation are number of bedrooms, presence or absence of private shower, and type of roof. Based on these characteristics it is possible to further generalize seven groups into three. The top four groups form a unique part of the image and consist almost entirely of one room homes, QUALITY 1. Groups 5 and 6 fit together on the image and show that two bedroom homes dominate each sector, QUALITY 2. Group 7 seems to stand on its own, QUALITY 3, with best housing quality attributes and the largest homes. A large number of all black and all white columns express a lack of variation. Data structure suggests the entire Riobamba population is provided with city services such as water, drains, trash pickup and electricity. In contrast, Ibarra has some small areas which are not served. This may be a result of annexation of residential areas north of Ibarra which, due to higher elevation and distance, are not served by water or electricity. In Riobamba, an under-bounded city, the built up area extends beyond the city limits. Additional residential areas outside Riobamba city limit, had they been included in this dataset, would have resulted in a data structure similar to Ibarra (e.g., lack of services in outlying areas). Defining urban limit is problematic when using government data to analyze urban structure because political boundaries dictate data collection. Thus, data limitations must be considered when drawing conclusions about availability of city services in Riobamba. Data structure suggests seven groups. For reasons just outlined, there is no group named In Town With Limited Urban Services in Riobamba. QUALITY 1 is interpreted visually to include the top four groups of Figure 4. Oneroom homes make up Group 1, Room Rent. Unique categories here are common bathroom and rooms for rent. It is the only group with all metal roofs, all renters, all floorboards, one room and one bedroom homes with private showers. Group 2 Metal Roof Owners has no unique characteristics; however, it is the only group which is 100 percent owners. The group is entirely detached homes with floorboards and private bathroom. Most homes have metal roofs and one bedroom. Group 3 Small Poor has slightly more renters than owners and all modal values are cement roofs. Most homes are detached with one or two rooms, excluding the bathroom. Group 4 is All One Bedroom. QUALITY 2 includes the next two groups. Group 5, called All Two Bedroom, has all two bedroom homes with private shower. There are a few apartment modal values in this group. Most are owned rather than rented. Group 6 is the only group with all three room homes, primarily detached with two bedrooms. There are a few apartment areas but most modal values indicate owners. This group was designated Good Quality, however, the second best group in Ibarra, Good Quality Big Home, consists of predominantly three bedroom homes, whereas in Riobamba Good Quality consists of primarily two bedroom homes. On average, better quality homes in Riobamba tend to be smaller relative to Ibarra. Group 7 is the only group with some five or six room homes and made up entirely of three bedroom detached homes with private shower. With higher than usual telephone service, this is the only group with predominantly asphalt composition roofs. Most modal values are owners. This group was tagged Best Quality Home, the only group in QUALITY 3. 7. INTERPRETING THE SERIATED IMAGE OF SANTA CRUZ Figures 5 and 6 present Santa Cruz binarized housing data before and after seriation. The matrix is 113 rows by 80 columns. Two variables not present in the Ecuador data are TVRADIO (presence of television and radio in home) and NEWS (frequency of newspaper delivery). Ecuador variable TELE (presence of telephone) is not in the Bolivia data. Since these are all means of communication and further define housing quality, they are included in the analysis. There are fewer areal units because Santa Cruz data is a sample, not a census.

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More variable categories suggest a more heterogeneous city, not surprising given Santa Cruz population is several times larger than Ibarra or Riobamba. The seriated data structure yields seven groups (Figure 6). Each has unique identity when interpreted column by column. In Santa Cruz, Group 1 is best quality housing. In considering merging, Groups 4 and 5 in the middle of the image fit together visually as QUALITY 1. Group 1 stands alone as QUALITY 3, with quite a few all black pixel columns. Groups 2, 3, 6, and 7, become QUALITY 2, with pixel distributions more alike than the other three groups. As in Ibarra and Riobamba, all Santa Cruz modal values have bottled gas available for cooking. In Santa Cruz there are no areal unit modal attributes predominantly apartments or hut type houses, whitewashed adobe walls, stone walls, cane or palm walls, or wood floors. Wood floors may be subject to deterioration and less popular due to lower elevation and more humid climate. Rainwater, river, lake or gravity flow water sources and firewood, guano, charcoal, or kerosene cooking fuel are absent, not surprising given the urban environment. FIGURE 5 SANTA CRUZ BEFORE SERIATION

FIGURE 6 SANTA CRUZ AFTER SERIATION Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7

Unlike the other two cities, for Santa Cruz, Group 1 is named Best Quality Big Home and is associated with higher-value homes designated as QUALITY 3. Group 1 has several unique characteristics, though fairly small in number (i.e., homes with four bedrooms, four rooms or three bedrooms). All group members have modal values for brick or cement walls, electricity, private bathroom, TV and radio, and separate room for kitchen. Approximately 80 percent are owners of detached homes which have public water, tile roofs, private shower, inhome water, trash pickup, and newspaper delivery seven times per week. Categorized here as moderate value homes (QUALITY 2), dwellings in Groups 2, 3, 6, and 7 are more similar visually on the seriated image to each other than to Groups 1, 4, or 5. All members of Group 2 have similar amenities, however, this group does not have any three or four bedroom homes; more than half of homes in this group are one room although all have a separate room for kitchen. Most are owners of detached homes with private shower and trash pickup. Although homes are smaller than Group 1 (QUALITY 3), they seem to have access to public services with the exception that in this group most have a water pipe outside of the home rather than piped inside the home. Group 2 is named Fair Services Small Home. Group 3, named Poor Services Small Home, is the only group which has no modal values of apartments. All are owners of homes, mostly detached with private bathroom, electricity, TV and radio. The group has no renters. There are no modal values for rooms for rent and fewer public services are available as indicated by lack of trash pickup, lack of public drains, and low incidence of newspaper delivery. Majority have public water available, although most do not

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have a private shower or a water pipe inside the home. Most have a water pipe outside the house and within the lot, although some must go beyond the lot for water. Homes are mostly small one or two room homes, and approximately 20 percent have predominantly earthen floors. Groups 4 and 5 were of the poorest quality housing (QUALITY 1). Low value residences in Group 4 consist of small one room homes which have no bedrooms or showers. Most are owner occupied detached homes with no public water pipe available, no separate kitchen and no newspaper delivery. Although most have a private bathroom, more often source of water is not a public system, but rather well water or other source of water. Some homes have earthen floors. This group was designated No Public Services. Group 5 is the only group that has improvised housing, adobe walls without whitewash, no tile roofs, no cement floors, and no separate kitchen. This is the only group in which all members have earthen floors and metal roofs. None have water pipe inside of home, a shower or a separate kitchen. All homes are owner occupied one room homes and most do not have electricity or public water. This group was named Earth Floor Poor. All members of Group 6 Rural Room Rent have electricity, TV, and radio, suggesting a better quality of housing than Groups 4 and 5. Nearly all members have rooms for rent with common bathroom, public water, no bedrooms and no separate kitchen. Very few have trash pickup and none have public drains, suggesting an urban environment lacking services. Group 7 All Rooms For Rent is the only group which predominantly rents from family, has no private bathrooms, no detached homes, and is made up entirely of rooms for rent, with common shower, and separate room for kitchen. Groups 6 and 7 fit best with Groups 2 and 3, which were designated as relatively moderate in housing quality or value, QUALITY 2. 8. CONCLUSIONS Nominal housing variables for three South American cities were analyzed using seriation. The technique identified indicators of relative housing quality and yielded an ad hoc three tier quality of housing index, a surrogate for income data that is not available in the Ecuador or Bolivia census. The index QUALITY 1, QUALITY 2, and QUALITY 3 (from lowest to highest property value) will be used as an explanatory ordinal variable with ratio type data as part of a larger project to explain generalities of density structure of South American cities. Each city was classified into seven or eight groups based upon visual interpretation of seriated images. Groups were further generalized to create a three tier relative housing quality index. (Table 1) Although groups were comparable within each city, they were only relatively comparable between cities, e.g., best housing in one city may be substantively quite different than best housing in another city. Mapping the derived three level housing quality index revealed that these three cities support the widely understood phenomenon that poor tend to live greater distances from city center, in contrast to most North American cities in which urban poor tend to reside closer to urban centers. Poorer residents in Ibarra, Riobamba, and Santa Cruz take advantage of lower land prices at the periphery while maintaining affordable bus access to urban centers. Apartment houses are not widespread in the three South American cities. Instead, rooms were rented or exchanged for services in homes or in rooming houses. Home ownership was associated with all levels of housing quality in all three cities. Figures 7, 8, and 9 are presented with approximate relative scale with north to the top and indicate schematically the distribution of housing quality and urban services based upon seriation of modal values of nominal housing quality variables. QUALITY 1 has the poorest housing and services and is shaded the lightest shade of gray, QUALITY 2 is a medium shade of gray and QUALITY 3, the best quality housing is black. Mapping supports the widely accepted characterization that Latin American cities have declining housing quality with distance from city center. Results also suggest correlation between political context and variability of housing quality. Of the three investigated cities, Riobamba exhibited the lowest

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variability of housing quality and Santa Cruz the greatest, in part because of size, but also perhaps the result of political context and public policy. The most homogeneous city, Riobamba, is a city managed by strong planning sanctions and socialist party government. The most heterogeneous seriated image is that of Santa Cruz, a city oriented to the service sector, with great extremes of wealth and poverty, a drug related economic base, and policies promoting entrepreneurialism. A seriated image indicating medium degree of housing quality heterogeneity, Ibarra, is a city managed by social democratic government. FIGURE 7 IBARRA

FIGURE 8 RIOBAMBA

FIGURE 9 SANTA CRUZ

A method involving visual graphic information interpretation, seriation offers a rich source of information for classifying and interpreting nominal housing quality data; is useful when ratio type data is not available; and provides results about distribution and clustering of various housing characteristics. Increased availability and quality of digital census data in South America combined with more powerful personal computing capabilities will increase value of empirical research using seriation from which new insights about cities will emerge. 9. REFERENCES Bertin, J.

1981. Graphics and Graphic Information-Processing. New York: Walter de Gruyter Publisher. Bjorke, J., and B. Smith. 1996. Geographic seriation: an implementation and a case study. Computers, Environment and Urban Systems 20: 427-438. Bjorke, J. 1989. Entropy as a tool for automated seriation. Unpublished manuscript, Trondheim, Norway: Department of Surveying and Mapping, University of Trondheim. Corporación Regional de Desarrollo de Santa Cruz (CORDECRUZ). 1988. Unpublished migration, employment, and housing survey for City of Santa Cruz, Bolivia. Santa Cruz: CORDECRUZ. Duff, A. 1996. Ceramic micro-seriation: types or attributes? American Antiquity 61:89-101. Dunnell, R. 1986. Methodological issues in Americanist artifact classification. Advances in Archaeological Method and Theory 9:149-207. Dunnell, R. 1970. Seriation method and its evaluation. American Antiquity 35:305-319. Helders, S. 2008. World Gazetteer. http://world-gazetteer.com Hodson, F. R., D. G. Kendall, and P. Tautu, eds. 1970. Mathematics in the Archaeological and Historical Sciences. Edinburgh: The University Press. Hurt, T.D., G.F.M. Rakita, and R.D. Leonard. 2001. Models, definitions, and stylistic variation: comment on Ortman. American Antiquity 66:742-743.

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Instituto Nacional de Estadística y Censos (INEC). 1992a. V Censo de Población y IV de Vivienda 1990 Provincia de Imbabura, Ciudad de Ibarra. Quito, Ecuador: Dirección de Informática. Instituto Nacional de Estadística y Censos (INEC). 1992b. V Censo de Población y IV de Vivienda 1990 Provincia de Chimborazo, Ciudad de Riobamba. Quito, Ecuador: Dirección de Informática. Lipo, C., M. Madsen, R.C. Dunnell, and T. Hunt. 1997. Population structure, cultural transmission, and frequency seriation. Journal of Anthropological Archaeology 16:301-333. Lyman, R.L., S. Wolverton, and M.J. O’Brien. 1998. Seriation, superposition, and interdigitation: a history of Americanist graphic depictions of culture change. American Antiquity 63: 239-261. Lyman, R.L. and M.J. O’Brien. 2000. Chronometers and units in early archaeology and paleontology. American Antiquity 65: 691-707. Mallory, J. 1976. Time perspective and proto-Indo-European culture. World Archaeology 8:44-56. Muller, J. 1983. Geographic seriation revisited. The Professional Geographer 35:196-202. O’Brien, M.J., and R.L. Lyman. 1999. Seriation, Stratigraphy, and Index Fossils: The Backbone of Archaeological Dating. New York: Kluwer Academic/Plenum Publishers. Ortman, S. 2000. Conceptual metaphor in the archaeological record: methods and an example from the American Southwest. American Antiquity 65:613-645. Petrie, W. 1899. Sequences in prehistoric remains. Journal of the Anthropologic Institute 29:295-301. SAS Institute, Inc. 1989. SAS/STAT User's Guide, Version 6. 4th ed, Vol 1. North Carolina: SAS Institute, Inc. Wrigley, N. 1985. Categorical Data Analysis for Geographers and Environmental Scientists. London: Longman.

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