18 Technique of Model-Construction in Geographical Studies

Prof Surendra Singh

1.0 Introduction:

Model building and generalization of geographical facts are important and significant issues which have been increasingly addressing with the use of ‘deductive’ explanation in the geographical studies. As geography deals with the spatial distribution of geographical phenomena, the construction of model is primarily concerned with three-dimensions of geographical elements, called 3-Ds:density, distance and division. The detail elaboration of these elements in geographical context is given below.

(a) The density of geographical phenomena, which refers to the size- area ratio – the amount and intensity of an attribute, varies across area over time. In order to analysis and interpret the spatial dimensions of such attribute, a variety of techniques are used. The concept, that forms the domain of geography, is integrally associated with two:

(i) The physical geography which includes many branches like geomorphology, climatology, bio-geography and oceanography on one hand, and (ii) the human geography that deals with the social, economic, demographic and locational aspects of the landscape of human activities (Singh 2013). The technique of spatial analysis of geographical phenomena is mainly focused on either phenomenal relationship or/and areal variation of the attribute(s) based on its density. It leads to a conclusion how areas/regions are tightly bound upto each other geographically.

(b) The Distance (Netorking and cost involvement): Analysis of location of a point/area becomes too important to make it more elaborative in its physical (natural resource base) and socio-economic (functional base of location of an attribute) contexts now-a-days when agglomeration/dispersion economies are ‘location-based’anddominate the activities in a region. It means that the ordering of space (spatial interaction) and organization of human activities (location-specific) for establishing economic as well as social activities are primarily ‘distance’ dependent. Distance involves the ‘closeness’ of producers and user in market activities which is viewed in three ways: physical distance in terms of money involved as geographical element of spatial organization of economic activities, distance in terms of time when distance between places is considered as development of network connectivity and, thirdly, the cultural distance when socio-cultural activities are more closely based on common language, modes of communication similar customs and social norms.

(c)  The Division: We are not indicating here the political division as country boundaries, but we are more concerned with the spatial organization of geographic entities and planning within a political unit (country). Space does not have plane surface; division of space is required to study features on account of spatial variation of economic activities, the geographical interpretation of attributes/variables follows its areal/regional characteristics. It involves a technique of division of space (physical or socio-economic). Physical divisions of the whole (geographic space) and/or classification of areal units to make spatial distribution of activities based on ‘similarities-within’ or ‘disimilarities between’ the areas involves the policy decisions in Regional Planning. Thus, division of space involves the policy implications. Further, division of space is a technique which leads us towards logical classification called ‘regionalisation’.

2.0 Model Building:

2.1 Model building is a Procedure for the Development of a System:

The followers of modern route of scientific research find generalization of facts proceeding through imposing the ‘hypothesis’ and its validity testing either by using ‘already-built model’ or by constructing a ‘new model’ considering the scientific route (development of proposition, imposition of conditions, use of axioms and assumptions and, later on, calibration and validation of model) to reach closer to the real world situation. Therefore, model-building involves a specific procedure and steps as given in detail in the next part of present discussion. Construction of a model for the solution of a research problem is to search a quantitative procedure of selected variables required for obtaining the problem-solution in its significant manner.

2.2 Model is a Tool-box:

Since a research problem is multi-dimensional phenomena, it is tackled with a variety of tools to transfer unordered facts into ordered-one to make generalisation.Model, thus, works as tool-box. If we have modern tools and techniques, our model-building is more scientific and such newly built models work better to search realities. In the book ‘Models in Geography’ authored by Chorley and Haggett, they clearly state that models are reflection of reality of an object. We must keep in mind that tools which fit the purpose to infer realities are to be used in model building, otherwisewe should not expect the correct results. For example, the statistical models are tested always with their significant-tests. If a quantitative model does not fit in reality, we must replace it and use another form of the model. For instance, suppose a linear equation for establishing relationship between the trend of Y subject to X variables, Y = a+bX, does not explain the facts significantly as we use ‘standard error’ term toexplain variation in the distribution, the non-linear equation as polynomial function may be used. If we compare the results of these two functions linear and non-linear and wish to opt one out of these two, we will have to keep in mind the error term. Smaller value of error gives greater degree of reality shown through the model. So, the choice of model for generalizing facts is largely dependent on error term to understand the significance of reality. As a result, model provides a strong base to reach closes to reality objectively.

2.3 Models are used to SystematiseRaw Data Set:

A given set of unordered facts in the form of quantitative data collected from the research field cannot provide the general information until it is converted into a scale through which it can be attributed for inferences. Model is the tool through which unsystematic data is systematized. For example, suppose we have rice yield and rainfall data of few stations of an area. If it is depicted by a scatter diagram, the regression tendency of yield, Y, subject to rainfall X may not be in a linear trend model. Following linear-trend model, it is supposed to be the distribution is linear. The computed values of yield, Yc are used instead of observed one, Yo, because these values are considered more systematic than Younless we know the error term of the model used for the purpose.

3.0 Aspects of Model-Building:

One must be careful at the time of construction of model when model are made for a specific purpose. It (model construction) requires quantified variables, controlled variables with relaxed ones (dependent-independent variables), aggregated view of variables, time concept also to be treated if required, tools and techniques used, relevant data available and inferences of main traits for generalization and development of laws. Such steps of the procedure of model-construction are discussed below in detail:

Step-1:

Purpose behind Model-Building: As per the research problems and issues taken up for solution, we have to determine the purpose of model-building to prepare an alternative strategy for the solution and to provide deductive explanation.

Step-2:

Quantification of Variables: Since one has to deal with the research problem in quantitative manner, the field work and data collection of objects are major tasks to frame research design. Imposition of hypothesis and prove it are dimensions which compel us for selection of attributes and variables. Variables are to be in quantitative manner in the tabulated form for further operation. Scaling of selected variables is primary task for model-builders to look into the problems.

Step-3:

Controls onVariables: When model-builder is going to analyse the system,‘causality’ is main principle keeping in mind that the answer of our research problem will be given logically. Cause-effect relationship is to establish by classifying variables into two categories, namely, the effect variables (dependent or base) and cause-variables (independent or factor). Say for example, crop yield is controlled by rainfall; we wish to establish relationship between cropyield and rainfall. Crop yield is dependent (variable) on rainfall (Independent).

Step-4:

Time Concept: Geographical studies follow space-time concept. One must include time as factor, if required, in the model construction. For example, if the development of model is towards the analysis of spatial development of socio-economy of a region, a set of four processes of development; barrier, hierarchy, network and contiguity considering as elements of space are taken into account with their different stages of time (Fig.-1). Sometimes, we do not consider time dimension if our study is based on one-time scale and our data collection schedule do not include time dimension. The dimension of space in model building is used in a variety of ways. A modern quantitative way of understanding spatial pattern of an attribute has many steps like preparation of a map of the surveyed area and showing location data of activities collected from samples (called spatial data). Such spatial data are depicted into geometric manner into zone system and particular zone is notated by number or algebraic symbols (Fig- 2).

Fig.-1: Spatio-Temporal View of the Development of Economic Landscape

Fig-2: Generation of Spatial data Collected from the Study Areaand its Depiction into Geometric Manner:

(A) real Map of the part of Delhi, (B) its Geometric Grids, and (C) Algebraic notation by letters Developing a good notation mathematically, a map-area is to show in coordinates following GIS for accurate and speedy calculation and depiction of spatial features of variables. Such type of data depiction of objects given on map into its geometric form provides a sound base to reach closer to reality. The data generated into a coordinate form can easily be used for the purpose through GIS tool.

Step-5:

Techniques used for Establishing Cause-effect Relationship:

Choice of technique is based on the following three dimensions of its uses:

(a) Assumption– It focuses direct attention towards the objective of research. When one constructs the model, some interrelated statements related to research problem are to assume based on speculation.

(b) Conditions–That prepares a scale of the variability of variable. If we know the extreme conditions of variables, it must help in speculation of relationship between variables.

(c) Axioms– That are well-established facts which are used sometimes somewhere for establishing new relationships of facts.

(d) Relationship prevelant in the system– Relationship between two sets of variables acts as integral part of the system that we wish to develop. After assembling the parts (tools) of the system and knowing their

relationships, we reach to a point from where we may obtain the ‘output’ of a model. If we are able to study the system which has parts and their assemblage, we are called ‘mechanic’ who knows about the system. But knowing simply about the outer part of the system, it indicates the operator of the system called ‘driver’. Model builder is a good mechanic.

(e) Caliberation and Validation– It is the step which is useful for simulation (prediction) of events which we need to analyse.Before it, validity testing of a model is needed. As per the use of model situation, there is a variety of ‘deviation-based’ validity testing methods to use the significance level of model error. What is deviation based testing?Models deviation from observed data is based on its error term, For example, a linear model which establishes relationship between Y (dependent) and X (independent) variables has error term, e, as:

Yo= a+bX+e and Yc=a+bX, so

e = (Yo-Yc),

whereYo= observed and Yc= computed values of a variable, Y. It is expressed by substituting Yc function in Yo equation.

The error of a model is tested in many ways. Statistical testing of a model is particularly based on two types of variations: the explained variation which is expressed by degree of determinants, R2, and, secondly, the unexplained variations, that is expressed in its degree of significance measured by the student’s‘t’ test. However, for different purposes, the ratio of the ‘Sum of Squared Deviation’ with ‘mean sum’ is used.

Step-6:

Simulation:

When model is tested and ready to use, we can simulate the results of as event on the basis of generalisationthat is the out come of the model. Speculation of event and development of law based on generalization are major achievements of model-building. Note that this procedure of testing validity is imposed hypothesis through the use of model and explanation of real-world situation is primarily dependent on ‘deductive’ explanation.

4.0 Example:

4.1 Modeling Retail Sales in Delhi Urban Area:

4.1.1 Research Problem and its Articulation: Retail sale is a major urban activity which contributes subsequently the city’s economy. It is distributed ubiquitously and is found in each locality. Suppose our problem is intended to build the shopping centres in future to choose the localities where location of new centres may be proposed. We will have to consider solving this problem the cash flow from the locality (where population resides and creates sale-demand) to the destination of locality where shopping store/mall (supply centre) is located. Such problem of uneven distribution of population and shopping centres has these two economic variables (demand and supply of goods of retail sale). The third variable is ‘distance’ between the locality where demand is created and location of shopping store (a variable associated with attractiveness force). An associated variability is ‘cash flow’ from one locality to another one (showing intensity of sale) which is dependent on these above cited variables ‘expenditure on shopping in each locality’ may be used as ‘converter’ of total population into its sale term in each locality. Now, we are interested to know the spatial pattern of cash expenditure on consumer goods in each locality and its flow to the locality where shopping centre is located. In this process of articulation of problem of measuring the total demand and supply of consumer goods and its spatial pattern, sales of each locality is dependent on cash flow from one locality to the others.

As we are more concerned with the spatial data of retail sale, the actual map of locality boundary which is a tool for showing sale pattern is generated zone-wise (instead of locality-wise) to make it more general and operative with GIS to generate data of distance. This modification may be made by using either longitudinal-latitudinal system on which GIS is based, or coordinate (x,y) system. Zones are named locality-wise or signing geometrically number as name(i= 1,2,3,…, n). Note that i refers to a particular zone of residents and j is zone of shopping centre with the condition i=j (Fig-3). Size of zone and its total numbers are to be determined by the planner as per the size of whole study area or spatial resolution at which we wish to develop the spatial pattern of sale of consumer goods. Distance between a set of two zones, Dij, may now be measured by using vector or raster system to apply ‘Pythagoreous’ theorem for the point coordinates expressed as

Taking account of above cited and considering the steps as described in the preceding part of the present discussion, we can now consider the generation of variable and their relationships. When we know that irepresent the zone of the origin of flow of money and j for the zone of destination of flow, the flow of money pattern is from i to j.

4.1.2 Assumptions:

The Sale of consumer goods in a particular zone j is the function of intensity of flow of money, expressed as Sij and flow of money from one zone to another is function of distance Dij. A few assumptions generalized on distance-costs relationship and on shopping goods are used here as:

(i) Distance,Dij,is considered linear betweenith and jth zones.

(ii) Travel costs,Cij, are linear function of distance. It means Dijis proportional to Cij.

(iii) There is some amount consumers of a particular zone keep safely in their pockets, that isaij. They do not spend total money on sale which they have to reach tojth sector. It is also included in travel cost between one zone to another to buy goods and material.Thus, distance variable is included in the form of its travel cost and expressed as (Fig.-3) :

       

Fig.-3: Quantitative Concept of Distance

4.1.3. Conditions:

There are three conditions of cash flow from i to j zones:

(i) The cash flow from i to j is proportional to,α, the total money available for shipping expenditure in i zone which is dependent on the household’s income ‘ei’; indirectly sale in shops located in j zone are proportional to per capital income into total population Pi in i zone. So,

(ii) The cash flow ( i.e. indicative of intensity of spatial interaction through sale intensity from i to j is also proportional to the size of sale centreMj in j zone (factor of attractiveness) be expressed as

(iii) The cash flow (means sale intensity) from i to j zone diminishes as travel distance increases. It means it is proportional to distance but inversely as

4.1.4. Model and its Testing:

Under these assumptions and conditions of sale in shops located in i zone and using proportionality constant (Xproportional to Y may be written as X = KY where K is constant), the relationship of above conditions may be expressed as

If we observe now that the emerging form of relationship between the amount of sale among population size of shopping centre and distance, it follows Newton’s gravity model in Physics which also has a constant and interaction between two masses as

In the retail sale gravity relationship (Eqn-6), the coefficient may be used to make this theoretical equation more applicable for different areas. The real form of retail gravitation, which is similar to Reilly’s law of retail sales, is as

Where α , β and n are coefficients in relation to population size, sale size and distance. A lineared form of the above constructed model is

It is obvious to say that the sale of consumer goods in a zone (i.e., locality) increases logarithmically (since coefficients operate in power function) as population as wellas shopping centre sizes increase and it decreases as distance increases.It is log- log distribution of attributes. There has been a deviation of observed figures of sale in each zone, Sijo, from predictedone, Sijp, which is calculated through the Equation (8). The smplest measure of such deviation is ‘the Sum of Squares’as used here with double summation sigh as

where e =error term; if e is zero, there is no deviation. Such variation may be tested by using any significant test as described some where else in the module entitled ‘Basic sampling and Test of Significance for Large Samples’

4.1.5 Model Utility:

There are three main dimensions to use this model of retail gravetion as given below:

(a) Since the model predicts the sale of consumer goods in each zone and generalizesits spatial pattern, it can be used as logical deductive explanation of sale pattern to understand the areas of fast supply zones to expand sale counters/shops in the city.

(b) The future requirement of shopping centres is demand-based; increasing population and/or increasing per capita income in i zone, eiPi, increase demand of sale counters/centres. If model is caliberated by changing its coefficients and constants as per the increasing demand of zones, the retail sale amount as well as location of shopping centres may be simulated to develop its new spatial pattern future. Therefore, it would be useful for development of infrastructure in the city to make proper city-planning.

(c) The total sale at jth zone for whole area is

The prediction of such sale of the area can be used as bench-mark for infrastructural planning of a city.

5.0 Summary:

There are two approaches of writing a report on research issues/problems; the ‘pattern’ approach when data of attribute(s) are collected, processed and classified to understand the facts and, second is the ‘system’approach through which we wish to understand the process and the working of the internal assemblages of the parts of a system and to know about its output. Model building is the main aspect of the second approach through which a deductive explanation and generalization of facts is proceeded by using hypothesis/hunches/assumptions/specific conditions and so on. Such explanation leads us towards construction of law and theories.

References

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• Burrough, P.A & R.A. McDonnell (1998): Principles of Geographical Information Syatems, Oxford University Press Inc., New York.
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