The Classification of Quality of Life Using Multi-criteria Analysis

Transcription

1 Journal of Geographic Information and Decision Analysis, vol.3, no.2, pp.1-8, 1999 The Classification of Quality of Life Using Multi-criteria Analysis Bryan H. Massam Department of Geography and Division of Social Science, York University, Toronto, Canada Contents 1. Introduction 2.The generic QoL classification problem 3. The Aspiration Interaction-level Model (AIM) 4. Analysis of hypothetical data 5. Conclusions References ABSTRACT After a brief review of selected literature on quality of life (QoL) the paper considers the use of multicriteria analysis for classifying individuals using data for a set of independent factors. A generic QoL classification problem is defined. A review and critique of a standard multi-criteria procedure which uses a simple additive weighting (SAW) model is provided. The problem of determining weights for factors for use in a SAW model is identified. Using hypothetical data for 11 individuals and 9 factors relating to quality of life a multi-criteria method which does not require the user to stipulate explicit weights for the factors is used to provide a classification of the individuals. The classification ranks the individuals in terms of their QoL from best to worst. Reference individuals are included in the data set to interpret the results. The method is the Aspiration-level Interaction Method (AIM). The merits of AIM for assisting policy makers determine allocations of resources among factors to improve QoL are presented. Alternate scenarios for allocating resources among factors are evaluated. KEYWORDS: quality of life, multi-criteria analysis, simple additive weighting model, aspiration interaction-level model, resource allocation, policy making. 1. Introduction Public policy-making in the fields of social services often focuses on the protection and improvement of the quality of life (QoL) for individuals and communities. Recent studies on QoL include surveys undertaken by the United Nations Development Programme at the aggregate level of the state to provide a ranking of states in terms of a Human Development Index (HDI). Details regarding the HDI are available on the website ( This index is calculated using empirical scores on three basic indicators relating to education, health and income. A simple additive weighting (SAW) model is used to calculate dimensionless scores using standardized values of the raw data.

2 A number of other studies using objective and subjective indicators for a variety of observation units such as census tracts, cities and regions have been reviewed by Murdie et al. (1992). Typically many of these studies use approaches based on economic, social, political and environmental indicators, and they rely on SAW models to produce maps of well-being, livability, sustainability and QoL. Smiths (1974) work on social indicators to identify areas of deprivation in cities, for example, is well known as part of his welfare approach to human geography. GIS are now used to produce maps of well-being and QoL. The causative linkages between objective and/or subjective scores, levels of performance or satisfaction levels on indicators and well-being, social needs and outcome levels for individuals in terms of health, education, economic prosperity, happiness, the capacity to cope and take control of life chances and opportunities, have been explored by a number of researchers. A variety of empirical studies on QoL in urban areas around the world is presented in Yuan et al (1999). A large-scale study on QoL of citizens in Ontario has been undertaken by a team at the Quality of Life Research Unit at the University of Toronto. Details are available on the web site ( Another web site ( provides useful information on a current study in Toronto on the QoL in the city and a number of linked websites offer complementary information on a wide range of QoL studies. The QoL study at the Quality of Life Research Unit (Brown et al 1998) uses a detailed questionnaire distributed to selected individuals who provide responses to a 5- point scale concerning the importance of specific indicators and the level of satisfaction for each indicator. A value greater than 3 for an indicator suggested a positive contribution to QoL, whereas a score of less than 3 contributes negatively. A score of exactly 3 is neutral. Contextual information is provided by asking each respondent to comment on their opportunities and control over life-styles. The indicators are defined and organized in such a way as to reflect three fundamental dimensions of QoL of an individual namely, being, belonging and becoming. These three dimensions are each divided into three characteristics and each of these is described by a number of indicators. Elaboration of these important terms on the "nine areas of the life" is included in the questionnaire (Brown et al 1998, p. 1). In this paper I will outline a generic quality of life classification problem in a way that allows it to be tackled using multi-criteria analysis. One specific type of analysis will be used to classify a set of observations using a hypothetical data set which comprises eleven individuals and nine indicators. Whereas many multi-criteria classification techniques require explicit data on the relative importance of the indicators expressed as a set of weights, or a pair-wise comparison, the technique used in this paper does not require this information. The technique to be used is the Aspiration Interaction-level Model (AIM) as developed by Lotfi et al (1998). Following this introduction the next section of the paper will offer brief comments on the general problem of classifying QoL of individuals using multi-criteria analysis. This will be followed by a description of AIM. The results of the analysis will be offered with general conclusions regarding the merits of multi-criteria analysis for tackling the generic problem and assisting in the evaluation of public policy-making which focuses on improving quality of life. 2

3 2. The generic QoL classification problem The problem can be stated thus: Given a set of observation units, for example, states, regions, cities, census tracts or individuals (I 1.I N ), and a set of factors, indicators or criteria which characterize independent components of QoL (F 1 F k ), and for each an achievement score (Sij - score for individual i for Factor j) combine the scores for all factors into a single QoL score for each individual. Among the information required to tackle this problem has to be included: the importance of the factors, for example, are they all equally significant in contributing to QoL? the type of data used to describe the scores: ranks, ratio data, non-commensurate values etc. the procedure for combining scores-additive, multiplicative, cumulative etc. Overall it is important that the procedure used for tackling the problem be transparent, so that the analysis can be replicated and it is traceable. Further, it is necessary that the arguments and logic of the procedure be credible in order that legitimacy be enhanced and so that those who use the results have faith in the exercise. Finally, in order to assist public policy-making it is useful to provide information on QoL in such a way that alternate policies can be evaluated and compared, and a preferred policy defended. With this in mind, if we have alternative rankings of individuals using different policy scenarios regarding the weighting of the factors then it is possible to determine which individuals benefit or suffer under each policy. This approach typically uses aggregate analysis as the same set of weights is assigned to the factors by each individual. The SAW model is often used to tackle the generic QoL classification problem. The justification relies on a number of assumptions, for example, that the raw objective data or the subjective data can be made or are commensurate, so that a compensatory model can be applied. Recently Malczewski (2000) has review assumptions regarding linear models as used in GIS. Hwang and Yoon (1981, p. 99) suggest that the "simple additive weighting (SAW) method is probably the best known and very widely used method of Multi-Attribute Decision Making". While we might contest the legitimacy of using a simple additive function for combining scores in order to obtain a single value for each individual it has been argued by Hwang and Yoon (981, p. 103) that "theory, simulation computations, and experience all suggest that the SAW method yields extremely close approximations to very much more complicated non-linear forms, while remaining far easier to use and understand". An interesting review of the errors which can be associated with the use of SAW models is given by Rowe and Pierce (1982). They use hypothetical data and introduce errors of known types and magnitudes in an attempt to determine "in a general way the sensitivity of the weighting summation decision model to some of the classes of error to which it is subject." For those who rely on the use of SAW to tackle the classification problem it is most important that clear recognition of the potential errors be incorporated into the study, and specifically that sensitivity tests be run as part of the analysis. Solomon and Haynes (1984) also conclude that while there are a variety of models for accumulating impacts into a final score, "the use of the simple weighting summation 3

4 model is probably justified." It is the use of a formal single dimensionless number which causes considerable problems for anyone who wished to use the results and participate in a debate which involves compromises, trade-offs and a discussion of scores and tradeoffs among factors. The aggregation of impacts across a wide range of variables is worrying to policy makers. Some argue that the score for a particular individual is not a simple additive function of the worth of the various components or even a readily identifiable multiplicative function, for that matter. This is stressed in a paper by Roy and Bouyssou (1986). In philosophical terms we are reminded of the debate propounded by Moore in Principia Ethica when he argued that "the worth of what he termed an organic whole bears no regular proportion to the sum of the values of its parts". In particular, "the value of a whole must not be assumed to be the same as the sum of its values of its parts" (Rosenbaum, 1975, p. 127). Yet this concern does not seem to hinder the development of the additive models. However, we can observe that there appears to be limited dialogue between theoreticians and practitioners in this area. One or two notable examples of cooperation should be mentioned, for example, the work of Keeney (1972) and the examples provided by Edwards (1971). We should further note that if we wish to defend the use of a simple additive model the following two conditions should be satisfied. First, the preferences for, or the tradeoff for pairs of factors, for example F r and F s should be preferentially independent of fixed levels for any other factors, for example F t. Second, that F r, for example, should be utility independent of the other factors. Intuitively these conditions are appealing however very rarely are they verified prior to the application of an additive model. One case of verification is given by Keeney and Nair (1977) in their study on the use of a set of six criteria for evaluating nine alternate sites for a nuclear power plant in the Pacific northwest of the U.S.A. They use the Multi Attribute Utility Theory approach. The verification of the two conditions depends upon the confidence we can attach to opinions regarding the trade-offs among factors at hypothetical levels. These types of questions are obviously not easy to pose in manageable practical ways to the various interest groups. The SAW model requires a set of weights for the factors, and one of the challenges facing the analyst is to justify a particular set. There is no single agreed methodology for determining the so-called correct weights. Alternate strategies for determining weights are reviewed in Massam (1993). Intuitively and experientially it is clear that not all factors are of equal importance in their contribution to QoL, yet the problem remains as to how best to determine an appropriate set of weights that accurately reflect preferences and opinions. In the next section the multi-criteria technique AIM is described and this technique does not require explicit weights for each factor to be defined at the outset. 3. The Aspiration Interaction-level Model (AIM) Basically this model requires three pieces of information for each factor: an ideal value (I i ), a nadir value (N i ) and a desired/acceptable or aspiration value (A i ). Scores for each factor for each individual are required. It can be argued that I i and N i represent maximum and minimum scores (best or worst scores) for each factor, while A i can be set to reflect a subjective level or achievement which is aspired to. For example, if A i = I i this implies that a lot of importance is attached to the factor i and a high weight should be assigned. However, if A i = N i then the reverse is the case. "The idea of the approach [AIM] is based on... the concept of a satisficing solution rather than... the traditional optimal 4

5 solution. Levels of aspiration are used to explore the set of non-dominated solutions, see Giocoechea et al. (1982) by having the decision maker establish levels of aspiration and then obtain some feedback about the reasonableness of these levels and the alternatives satisfying them... The nearest solution [to the aspiration solution] is defined as the alternative that minimizes a scalarizing function proposed by Wierzbicki (1979); with a weight on criterion i given by (A i -N i )/(I i -N i ), where A i is the aspiration level, N i is the nadir value, and I i is the ideal value for criterion i." The nearest solution is then an alternative that minimizes the expression with d i = (A i -N i ) (A i -x i k )/(I i -N i ) 2 and, positive but small, where x i k is the value of alternative k in terms of criterion i. See Lotfi et al (1988) for more details." (Lotfi 1989, p.14). Alternate values for A i can be used to describe different policy scenarios. For example, if it is assumed that all the factors are equally important then A i can be set to I i for each factor, however if it is felt that those factors concerning being are of no importance then for these factors A i can be set to levels at N i, or close to this. Under different scenarios perhaps different ranking of the individuals may result and this information can be used to assess alternative policies. For instance if certain individuals rank high when a particular set of factors is weighed heavily then a policy that focuses on improving these factors will yield benefits to these individuals. Table 1 Hypothetical data set Being Belonging Becoming F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 I I I I I I I I I I I Note(1): A score of 5 on a factor is the highest value and contributes positively to QoL. A score of 3 represents a neutral contribution to QoL. A score less than 3 represents negative contributions to QoL. I 9 : has the overall highest QoL with 5 for each factor. I 8 : has the overall lowest QoL with 1 for each factor. I 11 : is a marker individual separating, positive from negative scores for QoL 4. Analysis of hypothetical data A hypothetical set of data is given in Table 1. There are eleven individuals and the nine factors are grouped into three sets to represent being, belonging and becoming, following the concepts presented by Brown et al (1998) mentioned earlier. Using the data 5

6 in Table 1 four experiments were conducted under different assumptions regarding the aspiration levels for the factors. Each experiment generated a different ranking of the individuals from the highest to the lowest QoL. Details of the experiments are given on Figure 1 with the results. If all factors are equally important then only three individuals rate better than the marker I 11. However, if emphasis is placed on specific groups of factors, while setting the aspiration level to 3 for all the other factors, then many more individuals appear to have an overall positive quality of life, that is a score superior to the marker I 11. If emphasis is placed upon the three factors concerning being (F 1, F 2, F 3 ) then individuals I 2, I 10, I 3 and I 8 have negative QoL scores. For experiment 3, which places emphasis on the factors concerning belonging (F 4, F 5, F 6 ), individuals I 1, I 4 and I 8 have negative QoL scores. Finally, for experiment 4 which, places emphasis on F 7, F 8 and F 9, the factors relating to becoming, individuals I 1, I 10, I 5 and I 8 have negative QoL scores. On Figure 1 lines to join individuals for each experiment indicate the shifts which occur. While I 9 and I 8 occupy the stable end positions as best and worst QoL respectively the variations in markings are interesting. For example, only individuals I 6 and I 7 have positive QoL scores for all experiments. I 10 is consistently low, only for experiment 3 is a modestly positive QoL score recorded. I 2 moves from negative values for experiments 1 and 2 to very positive scores for experiments 3 and 4. Figure 1. Classification of individuals: four experiments; Experiment 1: all factors equal (A i = I i ); Experiment 2: F 1, F 2, F 3 set to ideal value (5) other factors set to 3; Experiment 3: F 4, F 5, F 6 set to ideal value (5) other factors set to 3; Experiment 4: F 7, F 8, F 9 set to ideal value (5) other factors set to Conclusions The significance of the shifts in ranking provides useful information for policy makers. For example, if a finite set of resources is available to allocate among the factors to improve QoL then the question is what proportion should be allocated to each factor to 6

7 achieve the greatest improvement in QoL? If we assume the total resource to be allocated is unity 1.0, then the allocation to the factors can be represented by the weights assigned using the AIM algorithm. For experiment 1, the weights for each factor are (0.111). The sum is unity. However, for experiment 2, 3 and 4 the weights assigned to the most important set of three factors is (0.167x3), while the other factors receive (0.083x6). the allocation of weights that generates the least number of individuals with positive QoL scores is the "all equal" experiment that allocates resources equally among all the factors. If resources are allocated to one of the three clusters that focuses on being, belonging or becoming then many more individuals enjoy positive QoL scores. Experiment 3 is perhaps the preferred one in terms of generating the largest number of positive QoL scores, though individuals I 1, I 4, and I 8 remain with low scores and probably deserve special individual attention. In summary I suggest that AIM is a useful multi-criteria technique to classify individuals in terms of scores for independent factors relating to QoL. A particularly interesting feature of AIM which makes it useful concerns the ability of the user to assign aspiration levels for each factor, and hence avoid the difficulties of defining explicit weights or measures of importance for the factors, which is a key part of the SAW method. By conducting a series of experiments with AIM using different aspiration levels to represent alternate policies then the effects on the ranking of individuals using QoL scores can be examined. From a public policy-making perspective it is important to link the descriptive aspects of multi-criteria analysis to prescriptive approaches which help to use public resources more effectively. I suggest that a multi-criteria technique like AIM has a useful role to playing in this regard.. References Brown, I. Raphael, D. and Renwick, R Quality of Life Profile, Adults (full version), Quality of Life Resources, Adult Series. Item #2-1, Quality of Life Research Unit, Centre for Health Promotion, University of Toronto, Toronto. Edwards, W "Social Utilities", Engineering Economics, Summer Symposium, Series 6. Giocoechea, A. Hansen, D.R. and Duckstein, L. 1982, Multi-objective Decision Analysis with Engineering and Business Applications, New York: Wiley. Hwang, C.L and Yoon, K Multi-Attribute Decision Making, New York: Spring Verlag. Keeney, R. L "Utility functions for multi-attributed consequences", Management Science, 19, Keeney, R. L. and Nair, K Selecting nuclear power plants in the Pacific Northwest using decision analysis, in Bell, D.E. Keeney, R.L. and Raiffa, H., Conflicting Objectives in Decisions, New York: Wiley. Lotfi, V "An aspiration-level interactive method (AIM) for decision making," Operations Research Letters, 8, Lotfi, V., Stewart, T. L. and Zionts, S "An aspiration-level interactive method for decision making", Working Paper #701, School of Management, State University of New York at Buffalo, Buffalo, New York. Malczewski, J "On the use of weighted linear contribution method in GIS: common and best practice approaches" Transactions in GIS, 4(1), pp

8 Massam, B.H The Right Place: shared responsibility and the location of public facilities, London: Longman. Murdie, R. A. Rhyne, D. and Bates, J Modelling Quality of Life Indicators in Canada: a feasibility analysis, York University, Institute for Social Research. Rosenbaum, S.P. (Ed) The Bloomsbury Group, Toronto: University of Toronto Press. Rowe, M.D. and Pierce, B.L "Some tests of analytical multi-objective decisionmaking methods", Socio-Economic Planning Sciences, 16,3, Smith, D.M "Who get What Where and How: a welfare focus for human geography," Geography 59, pp Wierzbicki, A.P "The use of reference objectives in multi-objective optimization, working paper # International Institute for Applied Systems Analysis, Laxenburg. Austria. Yuan, L.L. Yuen, B. and Low, C. (eds) 1999 Urban Quality of Life: critical issues and options, Singapore: School of Building and Real Estates. Acknowledgements This project was supported by a research grant from the Faculty of Arts, York University, Toronto, Canada. JGIDA vol. 3, no. 2 JGIDA Home 8