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6. Analytical methods and planning procedures

The integrated spatial-analysis methodology tested in the Bicol River Basin of the Philippines involved ten major components.

1. An overall regional resource analysis and socio-economic and demographic profile of the Basin that would serve as a data inventory for planning purposes and as a "baseline" study for monitoring and evaluation.
2. An analysis of the existing spatial structure, describing elements of the settlement system, the functional complexity and centrality of settlements, the hierarchy of central places, and the distribution of, and patterns of association among, functions within the region.
3. Description and analysis of the major socio-economic, organizational, and physical linkages among settlements within the Basin and between them and centres located in other regions of the country.
4. Mapping of information obtained from the functional complexity, settlement hierarchy, and spatial-linkages analyses to determine "areas of influence" or service areas of various settlement categories within the region.
5. Delineation of areas where linkages are weak or non-existent, and of marginal areas that are not served by central places or in which rural populations have poor access to town-based services and facilities that are crucial for rural development.
6. Comparison of information from the regional resources survey, settlement system, and functional distribution analyses to regional development plans and objectives to (a) determine the adequacy of the spatial system to meet development needs and facilitate the implementation of equitable growth policy, and (b) identify major "gaps" in the spatial system, in service areas for crucial functions, and in linkages among sub-areas of the region.
7. Translation of the spatial analyses into an investment plan that identifies the projects and programmes that will be needed to ameliorate major development problems, to strengthen and articulate the regional spatial structure, and to integrate various levels of settlement within it.
8. Integration of projects identified through spatial and economic analyses into spatially and functionally coordinated "investment packages" for different locations within the region, and combination of the investment packages into a priority-ranked and appropriately sequenced investment budget for the development of the region over a given period of time.
9. Creation of an evaluation system for monitoring the implementation of projects and programmes, and for determining the substantive results of development activities on marginal areas and population groups within the region.
10. Institutionalization of the planning procedures in local and regional public agencies charged with investment decision-making and with revising the spatial analysis and development plans at appropriate intervals.

This section of the case study reviews these ten activities in detail, describes the methods of analysis used in the Bicol River Basin, outlines the substantive findings and results of the analyses, and compares the techniques used in Bicol with those tested in similar projects in other developing countries.

An underlying assumption of the spatial analysis in Bicol was that it would be "problem oriented"; that is, the spatial analysis and planning would deal primarily with problems of stimulating growth with equity, and with providing essential information needed to make effective investment decisions. It was assumed that the spatial system in Bicol should be developed to stimulate "bottom-up" development in rural areas, facilitate the spread of growth from urban centres, increase the access of marginal groups to centrally located services and facilities, and use existing and potentially productive resources in ways that would benefit people living in the Bicol River Basin. The approach to planning would be developmental rather than adaptive, in that it would, as Hermansen describes it, "seek to identify and achieve within a dynamic and historical context a pattern of evolution of the spatial structure that at any point in time is judged to be most efficient from the point of view of promoting a sustained process of rapid economic development." Developmental spatial planning would attempt to create a spatial structure that would act as a catalyst for economic and social progress by transforming traditional organizations and patterns of interaction as development occurred.

Spatial development planning would seek to integrate and locate investments in such a way that they not only stimulate economic growth but also contribute to the evolution of an articulated and integrated spatial system capable of more widely spreading the benefits of growth to all areas of the region. Investments would be selected and located to enhance the capacity of various types of settlements, especially towns and cities, to act as service centres and catalysts of growth for rural development. As Babarovic notes of a similar experiment in regional development planning in Brazil, "location should be such that the accessibility of [urban centres] to the unincorporated rural population as a whole should be as great as possible in the marginated rural group."39 Moreover, it was assumed in the Bicol project, as it was in similar attempts at area development in India, that "an economic system works best and works in an efficient manner when appropriate linkages are established" among settlements of various sizes and that "the location and provision of missing infrastructure is a necessary exercise in regional spatial planning." But the project's advisers and designers also recognized that articulation and integration of the spatial system alone, although a necessary condition for equitable growth, would not solve the problems of marginality and poverty in economically lagging regions. Other government policies, which often allow exploitation of poor regions and subsistence populations, must also be changed so that the "terms of trade" between urban and rural areas, agricultural and industrial sectors, and traditional and modern occupation groups become more equitable.

Regional Resource Analysis-Data Inventory and Baseline Study

The Bicol River Basin Urban Functions in Rural Development project began with the preparation of a profile of socio-economic, physical, and demographic characteristics of the region. This analysis of regional resources would serve as an inventory of existing data, contribute to a comparative analysis of the region with other regions in the Philippines, and provide a baseline evaluation of conditions in the Basin at the time the project began.

Data were compiled and then disaggregated to provide a comparative profile of social, economic, physical, institutional, and demographic characteristics of Bicol's municipalities. Primarily descriptive, this aspect of the study made use of data on population size, density, and composition, levels of dependency, literacy, educational attainment, conditions of dwelling units, size of municipal revenues, land area, crop production, value of production, and experienced work force. Also included were comparative analyses of changes in population sizes of barangays, per cent distribution of population by municipality, number and per cent of households with lighting and toilet facilities, strength of construction of dwelling units, distribution of market receipts by municipality, and distribution of agricultural resources. The types, numbers, and distribution of productive and commercial establishments were compared by municipality as were the numbers and capacities of hospitals, educational institutions, and service establishments.

Constraints of time and money allowed little original data collection, which was not a serious problem in the relatively data-rich Bicol River Basin. But in other regions or nations without the extensive statistical base of Bicol, more primary data collection would have been required. Integrated spatial analysis of community development blocks (districts of from 60 to 80 villages) in India, for instance, was based on extensive original data collection at the village, household, firm, and shop levels using questionnaires especially designed to determine location-specific information. Village and household questionnaires were administered to every settlement within each block, and samples of households within each village provided detailed information on the location of services and facilities within the area and on socio-economic characteristics of families. Production, distribution, and other economic information was obtained from sample surveys of cottage industries, larger firms, and commercial establishments. In Bicol, however, these data could be derived from census reports, key informants, ministry studies, and from project feasibility analyses commissioned by the BRBDP. Most of the data were analysed by descriptive statistical techniques, and significant changes in conditions between 1960 and 1970, and 1970 and 1975, were calculated. Location quotients were derived for some of the economic and social data and others were used to form a quartile ranking of municipalities by relative levels of development.

1. Location Quotient Analysis. Location quotients are easily calculated indices of the relative specialization of settlements in specific activities or characteristics. They are especially useful for determining relative industrial or occupational specialization using employment as a surrogate for production. A location quotient is basically a "ratio of ratios" comparing, for example, the ratio of employment in a given industry or occupation in a municipality to employment in all industries in that municipality, to the ratio of employment in that industry in a larger reference area, such as a region, to all industrial employment in that region. The formula is as follows:

TABLE 3. Occupation Quotients, Selected Municipalities in Camarines Sur Province Compared to Bicol River Basin Area

where
Mi = employment in industry i in municipality
M = total industrial employment in municipality
Rj = employment in industry i in the region
R = total industrial employment in the region

A location quotient greater than unity indicates that the municipality or settlement is more specialized in that activity than the region, and implies that the settlement is performing an "export" activity. A location quotient of less than unity implies that the settlement is less specialized in the activity than the region, and may have to "import" services or goods to satisfy local needs. The occupation quotients for selected municipalities in the Bicol River Basin listed in table 3, for example, indicate that the municipalities of Naga City, Camaligan, Gainza, and Magarao are slightly more specialized in professional, technical, and managerially experienced workers than either the province in which they are located or the Bicol River Basin. Those municipalities that have occupational location quotients at or near unity are sufficiently specialized in those occupations to service local needs at their present levels.

A variety of socio-economic data can be analysed using the location quotient to determine relative specialization, and location quotients can be calculated to determine relative specializations in the region compared to the entire country. Moreover, a time-series of location quotients can be calculated to show changes in specialization among settlements over a period of time. Location quotients are very rough indicators, however, and must be carefully interpreted within the context of regional conditions and refined by the use of other analytical techniques. In Bicol the location quotient was of limited significance for analysing occupational or industrial specializations of municipalities because employment data were reported only at the provincial level and could not be disaggregated by municipality.

2. Quartile Bankings. The primary use of regional-resource survey information in Bicol was to determine differences in, and levels of development among, municipalities in the region. Municipalities were ranked by level of development based on three derived analyses: ranking of socio-economic and demographic characteristics associated with levels of development in the Philippines; ranking by share of industrial, commercial, and agricultural production establishments in Bicol; and ranking by transportation access, which was a function of the number of transportation outlets found in the municipality. Quartile rankings were done for selected socio-economic indicators and weighted rank calculations were used to cross-check the results with other analyses in arriving at three development levels of municipalities in the Basin.

TABLE 4. Socio-economic Profile of Municipalities in Bicol River Basin. the Philippines. 1970

Source: Government of the Philippines. National Census and Statistics Office. unpublished reports. 1970.

3. Substantive Findings. The analyses verified that, although the entire Bicol River Basin is predominantly rural, municipalities differ significantly in socio-economic characteristics. The distribution of services, facilities, infrastructure, and productive and social organizations among municipalities is highly skewed (Table 4). If these socioeconomic variables are used as indicators of development, municipalities in the Basin can be classified into three major levels.

a. Developing Municipalities include the six most urbanized, encompassing the two provincial centres of Naga and Camaligan, and Legaspi and Daraga, the city of Iriga and the town of Tabaco. Services, facilities, and productive activities are highly concentrated in these six municipalities, especially in Naga and Legaspi cities. The developing municipalities contain about one-quarter of the population /386,000 people or 22 per cent) but account for more than 40 per cent of the "urban" population; raise 45 per cent of the Basin's municipal revenues; and have significantly higher percentages of households served by piped water and electricity. Most of the Basin's educational and vocational training institutions are concentrated within them as are most of the major health care institutions. The developing municipalities contain nearly a third of all high school and 45 per cent of all college graduates in Bicol. They are the financial centres of the Basin, with nearly half of alt financial institutions and more than 85 per cent of deposit and loan assets. More than one third of all corn mills, agricultural warehouses, farm supply stores and farm machine and tool establishments, and nearly half of the cottage industries and commercial, financial, and service establishments are within their boundaries.

b. Less Developed or Transitional Municipalities are ten that lie at or near the Manila South Road within the central plain of the river basin. They are closer in socio-economic and physical characteristics to the underdeveloped municipalities than to the developing ones. But they are distinguished from the former primarily by the fact that their access to the Manila South Road or provincial arteries connecting them to the major cities of Naga and Legaspi has generated some diversification of economic and social activities in their pablaciones, and that they contain the potentially richest agricultural land in the Basin. This group of municipalities accounts for slightly more than 26 per cent of the population and has concentrations of services, cottage industries, infrastructure, and facilities slightly larger than its share of the population. Rural areas of these municipalities are largely underdeveloped: less than 20 per cent of households are served by piped water, they have few educational or health institutions, and commercial establishments are rare and scattered. Perhaps because of their physical proximity to the major provincial centres, these areas have not become highly specialized and seem to depend on the larger centres for marketing and trade.

c. Underdeveloped Municipalities include 38 predominantly rural, subsistence-agriculture areas forming the periphery of the Basin. Slightly more than half of the population of the Bicol River Basin lives in these municipalities, which, by all socio-economic characteristics, are the poorest and least developed. These 38 municipalities have a far smaller proportion of facilities, services, educated manpower, financial resources, and productive economic activities than their share of population. Their residents are scattered in rather small barangays. Only 8 per cent of households receive water and less than 6 per cent have electrical power. Only five of the 38 municipalities have post-secondary educational or vocational training institutions; nearly 40 per cent have no markets of any kind, and eight contain no financial institutions These municipalities collect less than two-fifths of all municipal revenues and, on the average, depend on the national government for nearly a third of their municipal income. Some of the municipalities obtain more than half of their revenues from the national government and have few sources of internal income. The financial institutions in these underdeveloped municipalities have less than 10 per cent of the deposit and loan assets in the Basin. As a group, these municipalities contain less than one-quarter of the manufacturing, commercial, financial and service establishments, only a little more than a third of agro-processing, storage and commercial establishments, and one-fourth of the health facilities.

Thus, the analyses revealed that a majority of the population in the Bicol River Basin lives in municipalities with few services or facilities needed to meet basic human needs or to increase agricultural production and expand non-agricultural employment opportunities. Moreover, they are generally isolated from or have extremely poor access to the municipalities in which services, facilities, and markets are most highly concentrated.

Analysis of Centrality, Functional Complexity, and Hierarchy of Settlements

This aspect of the analysis attempted to describe the existing spatial structure in the Bicol River Basin and to delineate the elements of the settlement system, the functional complexity and centrality of settlements, the hierarchy of central places, and the distribution of, and pattern of association among, functions within the region. As noted earlier, increasing the access of rural people to services and facilities located in towns and cities was considered important for incorporating marginal population groups and rural hinterlands into the regional economy. In many marginal areas resources cannot be mobilized and used for development because a spatial structure that facilitates the procurement, transformation, and delivery of those resources is not well-articulated and integrated. In marginal regions of some countries, central places that can support services and facilities requiring large market areas or higher population thresholds are neither numerous enough nor adequately dispersed to provide easy access for the rural poor. In other countries, as Johnson notes, the problem "is not that underdeveloped regions lack central places, for some have too many! What is amiss is that they rarely constitute a functional hierarchy, and for this reason they fail to provide an intermeshed system of exchange that will provide the requisite incentives for increased application of labor, capital and human skills."44 In most marginal regions, the population remains scattered in very small hamlets and villages that are incapable of supporting moderate or high threshold functions, of forming regular, institutionalized markets, or of allowing functional specialization and division of labour. Thus, there is little incentive for people in marginal areas to save and invest, seek productive uses for existing resources, or develop new resources. Opportunities for market expansion and nonagricultural employment are usually minimal.

The objectives of this phase of the analysis in the Bicol River Basin closely approximated those of the integrated spatial analysis undertaken in India, which as Shah points out were:

1. To study ... focal points of growth with ecological settlements coming within their ambit, and to suggest a scheme for the development of a hierarchy of growth centers for an efficient provision of goods and services;
2. To identify the functional gaps in the physical and institutional infrastructure of these centers and their related settlements and to meet their present and future needs; and,
3. Recognizing the varying patterns of resource endowments and likely trends and temporal patterns ... to plan alternative courses of action for the provision and development of various service facilities.

In the Bicol River Basin, the analysis was used to determine the extent and pattern of centrality, and the distribution, concentration, and ubiquity of services, facilities, and other developmental functions among settlements. The methodology included the following types of analytical techniques.

1. Functional Complexity Analysis of Municipalities Using the Guttman Scalogram. In regional analysis, the Guttman scalogram can be used to develop a cumulative scale of functions (items)-such as services, facilities, organizations, and establishments-and to rank settlements (cases) on the basis of the total number of functions located within them. In a perfect scale, each settlement would be expected to possess all functions of those places with lower or equal scores and would not be expected to possess those functions of places ranking higher in the scale. Assuming that a settlement's level of development is reflected in the number and diversity of functions located within it, relative levels of development for all settlements within a region can be determined by the array of scale scores. Combined with other analyses the Guttman scale can be used to group settlements into different levels of a hierarchy or categories of development and to depict relative levels of development within a region by plotting scale scores of each place on a map. Voelkner has used the scale scores, for instance, to classify settlements by degree of "modernization"-ranging from traditional villages with few functions through early transitional, late transitional, early modern, and modern, depending on the diversity and types of functions found within them. Scalogram analysis also indicates the centrality of settlements, assuming that centrality is the ability of a settlement to provide varied goods and services to less-developed areas.

The Bicol project initially attempted to extend the scalogram of municipalities that had been done earlier for Camarines Sur Province to the rest of the Bicol River Basin. The analysis by the Social Science Research Unit at Ateneo de Naga University was a typical application of Guttman scaling in regional analysis and clearly illustrates the procedure. First, a survey identified existing institutions, services, facilities and establishments in town centres (poblaciones) of each municipality. The items were coded as being either present or absent and scaled by the Guttman method. A computer programme arranged the towns in a scale, with those having the least number of functions scoring low and those with the most scoring high. The municipalities were then arrayed in a hierarchy of functional complexity and, based on scale scores, were regrouped into scale steps (Table 5). The 30 scale steps were condensed to nine and plotted on a map. Using the condensed steps as indicators of development levels of municipalities, cumulative isopleth lines were drawn around municipalities of equal levels of development (Fig. 4).

FIG. 4 Isopleth Map of Development Levels of Municipalities in Camarines Sur Province, Bicol River Basin

TABLE 5. Guttman Scale of Functional Complexity of Municipalities in Camarines Sur Province, Bicol River Basin, 1975

Source: S. Roco, Jr., and F. Lynch, "Development Levels in Bicol River Basin," SSRU Research Report Series, No. 17, unpublished draft, 1975.

The analysis clearly identified Naga City and Iriga as the most functionally complex centres in the province, delineated their apparent "areas of influence," and pinpointed the satellite or supplementary centres within those influence areas. The analysts found a strong correlation between transport access in settlements and their functional complexity, concluding that "accessibility coupled with complexity is a major factor in the evolution of a center" in the Bicol River Basin.

The Urban Functions in Rural Development project sought to extend the methods used in Camarines Sur to all 54 municipalities in the Bicol River Basin, employing 64 functions in eight categories-economic, social services, physical facilities, communications, recreational facilities, personal services, community organizations, and extension and protective services-identified in the SSRU's municipal inventory. The validity of using these items in Albay province was later verified by a sample survey of municipalities in that province.

Although this exercise provided useful information concerning the functional complexity and concentration of various services and facilities in municipalities-and strongly confirmed the findings of the quartile analyses of regional resource data concerning levels of development among municipalities within the Basin-its most important deficiency was that the municipalities in the Philippines are administrative areas and not necessarily discrete settlements. A second scale, of urbanized or "built-up areas," was done to rank settlements by functional complexity and delineate a hierarchy of central places. The built-up areas consist of (a) poblaciones and contiguous barangays with approximately the same land use characteristics as the poblacion, and (b) other barangays within the municipality with a population size of at least 50 per cent of the poblacion.

Neither the municipal nor built-up area scales, however, distinguished barangays as discrete settlements. Indeed during the surveys it became clear that many barangays, like municipalities, were only administrative areas rather than discrete settlements. And since accurate boundaries for many barangays could not be determined, population density criteria had to be eliminated. It was decided, instead, to test the census definition of settlements: poblaciones and other barrios with a population of at least 1,000 in which the occupation of the inhabitants is predominantly nonfarming/fishing and which have specified physical characteristics. All barangays not meeting these minimum population-physical facilities criteria were considered to be non-central places and would be treated as a group at the lowest order in a hierarchy of functional complexity. A survey was later done of all barangays, which confirmed the validity of this judgement. To get a better indication of the hierarchy and functional complexity of settlements, the staff turned to other methodologies, including a manual version of the Guttman scale for all barrios in Bicol.

2. Manual Scalogram Analysis of Settlements. The manual version of the Guttman scale is primarily a graphic and nonstatistical device that arrays functions by ubiquity (frequency of presence) and ranks settlements by functional complexity on a matrix chart. The Guttman scales calculated by a computer programme presented two major problems for analysis in the Bicol River Basin. First, the functions that seemed to be of most interest for rural development-farm-equipment repair shops, vocational schools, credit unions, rural banks, farm supply stores, etc.-did not scale and were eliminated from the scale scores by the computer. Second, the computer output was difficult to understand and could not be easily presented to show the distribution of functions by place. The computer version required detailed explanation and interpretation, which technically untrained policy-makers- at least those attending the Bicol technical workshops in which the method had been presented-found difficult to understand. Nor did they immediately see its relevance.

A graphic scale used successfully in India and Indonesia was adapted for the Bicol study. All settlements were included-a total of 1,419 built-up areas and barangays. The technique resulted in a graphic presentation illustrated in figure 5. Both data collection and calculation requirements for constructing a scalogram are minimal. They include:

1. a list of all settlements in the area under study (hamlets, villages, market towns, small cities, larger urban centres);
2. population size of all settlements in the area or region;
3. a map pinpointing the location of all settlements in the study area; and
4. an inventory showing the presence or absence of functions (services, organizations, facilities, establishments, or other activities) in each settlement.

The procedure for manually constructing a scalogram is as follows.

1. On the left side of a worksheet, list settlements as rows in descending order of their population;
2. across the top of the worksheet, list the functions found in the region in their descending order of ubiquity (frequency of presence);
3. draw row and column lines so that the worksheet becomes a matrix in which each cell represents a function that may appear in the settlement;
4. fill in with a dark colour all cells in which a function is actually found in a settlement, leave cells for which a function does not appear in a settlement blank;
5. reorder the rows and columns so as to visually minimize the blank cells appearing in the dark pattern found in the upper left section of the matrix;
6. the scalogram is complete when no shifting of a settlement row or function column can reduce the number of blank cells in this pattern;
7. the final order of settlement rows identifies a ranking of settlements which can be interpreted as an ordinal centrality score.

FIG. 5 Section of a Scalogram for "Built-Up Area" Settlements, Bicol River Basin

As Fisher notes, "the scalogram provides a visual description of the . . . settlement and institutional hierarchy that is easy to read and useful as a reference in analyzing numerous issues for planning." This observation was confirmed in the presentations at technical workshops, where both technically-trained personnel and local political leaders examined an initial version of the scalogram prepared for the 120 settlements at the "top" of the hierarchy. Moreover, as Voelkner observes of the application of scalogram analysis in Thailand, the Philippines, and Sri Lanka, it can "systematically process and measure qualitative data which previously permitted only intuitive analysis." It can also process quantitative data that are error-prone or not statistically reliable by using only their qualitative content, for which the error margin is low, and can serve as a substitute for quantitative analysis when reliable statistical data cannot be collected quickly or economically.

Among the potential uses of the scalogram in regional planning are the following.

1. It can be used to categorize settlements into levels of functional complexity and determine the types and diversity of services and facilities located in central places at various levels of a hierarchy.
2. The scalogram shows rough associations among services and facilities in specific locations and potential linkages among them.
3. The scalogram indicates the sequence in which settlements accumulate functions and the implications for sequencing complementary or catalytical investments.
4. By reading any column the ubiquity of a service or facility, and its distribution among settlements, can be easily seen.
5. The array of items in the scalogram, analysed in conjunction with a map showing locations of functions and their distribution and with population-service criteria, can be used to make determinations about the adequacy of services and facilities in the region.
6. "Missing" or unexpectedly absent functions are clearly identified and investigations can be made into the reason that settlements at that scale level do not have the services or facilities, and decisions can be taken about the appropriateness of investing in those functions.
7. Unexpectedly present functions are also identified, and the reason for the appearance of services and facilities in those settlements can be determined.
8. Rough indicators of population threshold size needed to support various services and facilities can be determined from scalograms that show the population sizes of settlements in which functions currently appear.
9. The scalogram can be used to make decisions about appropriate "packages" of investments for settlements at different levels in the spatial hierarchy.

Thus, a manual scalogram has definite advantages over the computerized Guttman scale for application by rural planners, since it is easy to construct and interpret, requires no sophisticated training or equipment, and can be easily updated and revised using either "windshield surveys" or good aerial photography. More systematic reporting schemes can be designed to obtain information about changes in services and facilities in settlements of a region, as has been done in the village headman surveys in Thailand .

3. Threshold Analysis. In order to obtain better approximations of the population sizes required to support existing services and facilities in the Bicol, the staff adapted MarshalI's approach to threshold analysis. Marshall argues that "the threshold is that size of center which divides the ranked list of centers in such a way that the number of centers lacking the function above the division is equal to the number of centers possessing the function below the division." The method is especially appropriate to analysis of rural regions and to the type of data already collected for scalogram analysis, in that it requires only a ranked listing of settlements and the presence or absence of functions. Marshall suggests a modification on the general rule: "Once a threshold has been determined, this threshold (and the function to which it applies), will subsequently be disregarded unless at least half of all the centers above the threshold size possess the function in question."

TABLE 6. Calculation of Threshold Levels for Central Place Functions

The staff adopted the procedure which is illustrated in table 6.

a. Construct a table with a rank listing of centres according to population, a corresponding list of population data and the presence (1 ) or absence (0) of every function in each of the centres listed;
b. apply Marshall's rule and identify each function's population threshold; and
c. apply Marshall's supplementary rule and disregard functions eliminated by this process.

There were, however, definite limitations on the use of this technique. Current threshold levels may not realistically represent the potential for settlements of various sizes to support services and facilities, and may reflect locational decisions not based on market considerations. They also fail to reflect development obstacles that may have prevented services and facilities from being efficiently located in settlements that do have the required population sizes to support them. The technique does offer a "quick and dirty" means of calculating the thresholds for currently available services and facilities, however, and was used in conjunction with other methods of estimation.

4. Weighted Centrality Indexing for all Settlements. Another complementary exercise to obtain an indication of centrality was the calculation of weighted centrality indices for all settlements. The staff devised a method of adapting Marshall's centrality index, assigning weights on the basis of ubiquity of functions. The procedure is as follows.

1. Reproduce the largest Guttman scale in an inverted form with cases arranged vertically and items horizontally;
2. total each row and column.
3. using the assumption that the total number of functional attributes in the entire system has a combined centrality value of 100, determine the weight or "location coefficient" of the functional attribute by applying the formula:

C = t/T

where
C = the weight of functional attribute t
t = combined centrality value of 100
T = total number of attributes in the system;

4. add one block to the table and enter the weights computed;
5. reproduce another table similar to that in step 1 displaying the weights calculated in step 3 and the total centrality values; then f. sum the weights of each row to produce the indices of centrality.

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