African Journal of Science and Research,2015,(3)7:15-19 ISSN: 2306-5877 Available Online: http://ajsr.rstpublishers.com/ A MULTIDIMENSIONAL SCALING APPROACH TO HUMAN DEVELOPMENT CLASSIFICATION OF AFRICAN COUNTRIES. Tugba Altintas Faculty of Business Administration, Istanbul Aydin University, Istanbul, Turkey. Email:tugbaaltintas@aydin.edu.tr Received:02 Jan,2015 Accepted: 02,Feb,2015 Abstract In this study, Multidimensional Scaling Analysis has been used to classify African countries in terms of human development. Indicators of Human Development Index have been taken as independent variables of the model. The main goal of this research is to compare development groups and member countries obtained from Multidimensional Scaling Analysis to the development groups based on UN s HDI rankings. Research findings showed that some African countries especially medium ones relocated due to the applied method. Then, it could be thought that Multidimensional Scaling Analysis represents another quantitative choice to classify countries. Keywords: Welfare and social development, human development index, Multidimensional Scaling, development classification, African countries. INTRODUCTION The human development index (HDI) is a composite index that measures the average achievement in a country with three basic dimensions of human development: a long and healthy life, knowledge, and a decent standard of living (UNDP, 2006). It was created in 1990, as an acknowledgment that income levels are not enough to capture the concept of human development (Aguna, and Kovacevic, 2010). The first Human Development Report introduced a new way of measuring development by combining indicators of life expectancy, educational attainment and income into a composite human development index, the HDI. The breakthrough for the HDI was the creation of a single statistic which was to serve as a frame of reference for both social and economic development (OPHI, 2011). The HDI sets a minimum and a maximum for each dimension, called goalposts, and then shows where each country stands in relation to these goalposts, expressed as a value between 0 and 1 (Antonoaie et al., 2013). Long and healthy life is quantified in the life expectancy at birth. It has been found to be an excellent and accurate measure of the total mortality of a nation, with the possible exception of the potentially significant influence of the infant mortality rate on its measurement (Morris, 1979). The life expectancy at birth as an indicator of HDI is calculated using a minimum value of 20 years and maximum value of 83.57 years. This is the observed maximum value of the indicators from the countries in the time series, 1980 2012 (UNDP, 2013). For education indicator, the expected years of schooling for a school-age child and the mean years of schooling for population aged 25 and above were combined using an unweighted geometric mean (Escosura, 2014). In the case of income, per capita Gross National Income (GNI) replaced GDP per capita, thus capturing the income accrued to residents of a country, rather than the income produced in the country. The HDI uses the logarithm of income, to reflect the diminishing importance of income with increasing GNI. The scores for the three HDI dimension indices are then aggregated into a composite index using geometric mean (UNDP, 2013). The new human development index also altered its goalposts for each dimension with upper and lower bounds corresponding to the maximum values observed during the period 1980 2010 and to discretionally fix minimum values, respectively (Escosura, 2014). Having defined the minimum and maximum values, the subindices-life Expectancy Index (LEI), Education Index (EI), and Income Index (II) - are calculated as follows (UNDP, 2013): Human Development Index, Based on the above calculation, countries have been grouped as "very high human development (HDI=0.900)", "high human development (0.800<=HDI<0.900)", "medium human development (0.500<=HDI<0.800)", and "low human development (HDI<0.500)" countries (Ferrer, 2009) by referring their HDI scores. Africa, a continent endowed with immense natural and human resources as well as great cultural, ecological and economic diversity, remains underdeveloped. Most African nations suffer from military dictatorships, corruption, civil unrest and war, underdevelopment and deep poverty. The majority of the countries classified by the UN as least developed are in Africa. African countries have been growing at a relatively fast rate since the beginning of the new millennium, which in turn has led to improvements in several areas such as trade, mobilization of government revenue, infrastructure development, and the provision of social services and vice versa. Indeed, over the period 2001 2008, Africa was among the fastest growing regions in the world economy, and it is interesting to note that this improvement in growth performance has been widespread across countries (UNCTAD, 2012). According to Human development report which has published in 2006, eighteen countries have a lower HDI score today than in 1990-most in Sub-Saharan Africa. Today 28 of the 31 low human development countries are in Sub-Saharan (Haghshenas et al., 2007). Table I shows development classes of 50 African countries according to their HDI scores for the year 2012 (UNDP, 2013).
16 Tugba Altintas Table (1). Development Classes of African Countries Developm ent Country HDI Score Very High Seychelles 0,81 Algeria 0,71 High Libya 0,77 Mauritiu 0,74 Tunisia 0,71 Botswana 0,63 Cape Ver 0,59 Egypt 0,66 Equatori 0,55 Medium Gabon 0,68 Ghana 0,56 Morocco 0,59 Namibia 0,61 South Af 0,63 Swazilan 0,54 Angola 0,51 Benin 0,44 Burkina 0,34 Burundi 0,36 Cameroon 0,5 Central 0,35 Chad 0,34 Comoros 0,43 Congo_D 0,3 Côte d'i 0,43 Djibouti 0,45 Eritrea 0,35 Ethiopia 0,4 Gambia 0,44 Guinea 0,36 Guinea-B 0,36 Kenya 0,52 Low Lesotho 0,46 Liberia 0,39 Madagasc 0,48 Malawi 0,42 Mali 0,34 Mauritan 0,47 Mozambiq 0,33 Niger 0,3 Nigeria 0,47 Rwanda 0,43 Sao Tome 0,53 Senegal 0,47 Sierra L 0,36 Sudan 0,41 Tanzania 0,48 Togo 0,46 Uganda 0,46 Zambia 0,45 As mentioned above, it could be thought that African countries have an immense development potential due to the national and human resources. In this context, it was also indicated that African countries have a relatively fast development rate over 2001-2008 period. Despite this, when we observe African countries HDI scores and development classes for the latest available year (2012), 35 of 50 countries are still low developed. Wonder if another method was used to obtain development classes of African countries instead of HDI, could we see different development classes and less low developed countries? Here is this question builds the main goal of this paper. There are various classification techniques under multivariate statistical methods. In this study multidimensional scaling analysis was utilized as a grouping method. The HDI indicators; life expectancy at birth, mean years of schooling, expected years of schooling, and GNI per capita were taken as independent variables. Data were obtained from World Data Bank belong to the year 2012, and attached in Appendix A. MATERIAL AND METHOD As mentioned in the introduction part, to obtain development classes of African countries, MDS analysis was applied. MDS represents measurements of similarity or dissimilarity among pairs of objects as distances between point of a low-dimensional space. MDS is a technique that makes data accessible to visual inspection and exploration (Borg and Groenen, 2005). MDS is carried out on data relating objects, individuals, subjects or stimuli to one another (Cox and Cox, 2010). MDS represents inter-object (dis)similarities by inter-point distances. MDS algorithms use the Euclidian distance model as a basis to compute optimal distances between objects in an n dimensional stimulus space. The related distance function, Euclidian distance, corresponds to our everyday experience with objects (Schiffman et al., 1981). While there are a variety of distance models that may be used in MDS, the one most frequently used is the Euclidean distance model (Zhang and Takane, 2014). It is also a metric faster than clustering with the regular Euclidean Distance and an efficient tool for clustering databases (Mouffron et al., 2008). The squared Euclidean Distance Measure is (Giguère, 2006); where; x =country x; y =country y; MYS = mean years of schooling; EYS = expected years of schooling; GNI = gross national income; LE = life expectancy. Classical MDS (CMDS) is a model which uses only one matrix of raw or averaged data, which is matrix conditional. When using this model, the algorithm produces a hypothetical Euclidian stimulus space which matches the original data as much as possible (Giguère, 2006). MDS doesn t require statistical distribution assumptions like cluster analysis, and it directly operates on dissimilarities (Wilkinson, 2012). The goodness of fit measure is called stress and can be calculated in several ways. But it is in fact a badness-of-fit measure because the higher the stress score, the worse the fit (Kruskal and Wish, 1978). A high stress value usually indicates that the chosen number of dimensions is not adequate for accurately portraying the complex relationship among a set of objects. An alternative explanation could be that the objects depicted have no real relationship and therefore cannot be arrayed in the number of dimensions chosen. Regardless, a high stress value is considered undesirable (Sturrock et al., 2000). Multidimensional scaling can be carried out for elements and constructs separately using ALSCAL in SPSS. ALSCAL is a multidimensional scaling (MDS) program with a number of individual differences options unavailable in other nonmetric MDS programs and it uses the Alternating Least Squares approach (Young et al., 1978). ALSCAL minimizes the S-stress, a measure
African Journal of Science and Research, 2015,(3)7:15-19 17 based on squared distances which emphasizes large distances relatively more strongly (Ossietzky, 2014). RESULTS AND CONCLUSION In this paper 50 African countries were classified by Classical MDS analysis. By using ALSCAL algorithm in SPSS 17, the Euclidean Distance was chosen as dissimilarity measure. At the end of ALSCAL iterations, S-Stress and RSQ values were found as 0,09 and 0,97 respectively for two dimensional solution and a very good fit was obtained. RSQ shows the variance explained and 97% of total variance was explained by two dimensions. Table 2. Stimulant Coordinates Stimulus Stimulus Dimension Number Name 1 2 1 Algeria 2,0031-0,6032 2 Angola -0,1061 0,4551 3 Benin -0,5318-0,1860 4 Botswana 1,5936 1,3741 5 Burkina -1,4606-0,3307 6 Burundi -0,8267-0,0114 7 Cameroon 0,0531 0,4835 8 Cape_Ver 0,8331-1,3794 9 Central -1,2918 0,3946 10 Chad -1,5550 0,1167 11 Comoros -0,3677-0,6055 12 Congo_D -1,0343 0,3798 13 Côte_d_I -0,9119 0,0701 14 Djibouti -1,0228-0,0800 15 Egypt 1,3652-0,7865 16 Equatori 0,8939 2,5424 17 Eritrea -1,3891-0,6889 18 Ethiopia -0,7625-0,5264 19 Gabon 1,8089 0,3819 20 Gambia -0,6224-0,2897 21 Ghana 0,7938-0,4499 22 Guinea -1,1315-0,3167 23 Guinea_B -1,1485 0,2970 24 Kenya 0,4904 0,1573 25 Lesotho -0,3517 0,7595 26 Liberia -0,2772-0,2352 27 Libya 2,9533-0,4802 28 Madagasc 0,2983-0,6706 29 Malawi -0,3293-0,0252 30 Mali -1,3635 0,0070 31 Mauritan -0,4931-0,1571 32 Mauritiu 2,3758-0,2687 33 Morocco 0,6145-0,9582 34 Mozambiq -1,3793-0,0226 35 Namibia 0,7641 0,0039 36 Niger -1,9134-0,1681 37 Nigeria -0,3863 0,3638 38 Rwanda -0,3785-0,2113 39 Sao_Tome 0,2639-0,4836 40 Senegal -0,3656-0,1956 41 Seychell 3,8383 0,5547 42 Sierra_L -1,2855 0,4298 43 South_Af 1,4749 1,0690 44 Sudan -1,4003-0,6711 45 Swazilan 0,2888 1,0299 46 Tanzania -0,1511-0,1279 47 Togo 0,0215-0,0876 48 Tunisia 2,0278-0,8020 49 Uganda -0,1064 0,0391 50 Zambia -0,4120 0,9099 The stimulant coordinates in Table 2 are the weights each variable has in a given dimension. In which dimension the country is strong, it has the higher value. For example Seychelles is the strongest country on Dimension 1, where Equatory appears high on Dimension 2. Fig(1). Countries on two-dimensional scale It can be seen from Figure 1, Seychelles is very much alone while other countries are clumped between close values on dimension 1. Hence, very high developed country class has also only one member according to the MDS analysis. Low developed countries obtained from UNDP s HDI calculation are also very close to each other according to the MDS analysis. Then, it could be accepted that the class of low developed countries was consisting of the same countries acoording to MDS like UN s class. When high developed countries are observed on Dimension 1, Algeria, Libya, Mauritiu and Tunisia are clumped between the values of 2 and 3. It shows that memberships of high developed country class didn t change at the end of MDS analysis. Egypt, Gabon, South Africa and Botswana are the medium developed countries and their HDI scores are 0.66, 0.68, 0.63 and 0.63 respectively. While their location has been evaluated on dimension 1they are closer to the high developed countries than the medium developed ones. Their HDI scores are already high when compared to the other medium developed countries. Then, this result could be accepted as the most important result of MDS analysis. Equatory, Cape Verde, Morocco, Ghana, Namibia and Swaziland are very close to each other and accepted the members of medium developed country class according to the MDS analysis. Then, it could be thought that they didn t change the location. In Table 3, development groups and memberships obtained from MDS were shown as a final list.
18 Table 3. MDS Development Groups Development Level Very High High Medium Low Country Seychelles Algeria Libya Mauritiu Tunisia Botswana Egypt Gabon South Af Cape Verde Equatori Ghana Morocco Namibia Swazilan Angola Benin Burkina Burundi Cameroon Central Chad Comoros Congo_D Côte d'i Djibouti Eritrea Ethiopia Gambia Guinea Guinea-B Kenya Lesotho Liberia Madagasc Malawi Mali Mauritan Mozambiq Niger Nigeria Rwanda Sao Tome Senegal Sierra L Sudan Tanzania Togo Uganda Zambia This paper aimed at studying how would development classes be in case of using MDS analysis instead of UN s HDI ranking. The component indicators (variables) without any additional variables were used in the analysis. In order to obtain development groups ALSCAL program was applied. All variables were standardized as z scores to eliminate the effect of outliers and variables different Tugba Altintas measuring units. The Euclidean Distance Measure was chosen as a dissimilarity measure. It was found that the classification into four groups is not stable like UN s groups based on HDI rankings. Very high developed country didn t change and it is Seychelles. Likewise, it was seen that the class of low developed countries includes same member countries. Middle and high developed countries were regrouped. Although Egypt, Gabon, South Africa and Botswana are the medium developed countries according to the HDI list, as a result of MDS analysis they were accepted as high developed countries. In summary, it has been thought that there is a positive effect of MDS method in terms of development classification. At the same time, the increasing number of high developed countries could be seen as a supporting and strengthening result for promising beliefs about African development. Findings showed that MDS analysis could also be used as a robust choice to group countries in terms of UN s HDI indicators. In addition, it is hoped that this study would contribute to the future studies about development and could be of use for both individuals and organizations in selection of countries to invest. References 1)Aguna, C., Kovacevic M., (2010) "Uncertainty and sensitivity analysis of the human development index." Human Development Research Paper, p.11. 2)Antonoaie, C., Antonoaie, N., Antonoaie V., (2013) "Environmental protection, sustainable development and corporate responsibility in wood industry. Part 1: environmental sustainability." Pro Ligno 9.4. 3)Borg I, Groenen P (2005). Modern Multidimensional Scaling: Theory and Applications. Springer, Second edition. 4)Cox, T. F., & Cox, M. A. (2010). Multidimensional scaling. CRC Press. 5)Giguère, G. (2006). Collecting and analyzing data in multidimensional scaling experiments: A guide for psychologists using SPSS. Tutorials in Quantitative Methods for Psychology, 2(1), 27-38. 6)Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling (Vol. 11). Sage. 7)Morris, D.: 1979, Measuring the Conditions of the World s Poor: The Physical Quality of Life Index (Pergamon, New York). 8)Mouffron, M., Frederic R., Huafei Z., (2008) "Secure Two-Party Computation of Squared Euclidean Distances in the Presence of Malicious Adversaries." Information Security and Cryptology. Springer Berlin Heidelberg. 9)Nader Motie Haghshenas, MA, Arezo Sayyadi, MA,Sahel Taherianfard, MA, & Nahid Salehi, MA Population Studies and Research Center for Asia and the Pacific Tehran, IRAN Submitted to UAPS, 5th African Population Conference, Arusha, Tanzania, 10-14 http://uaps2007.princeton.edu/papers/70300 10)OPHI, (2011) http://www.ophi.org.uk/wpcontent/uploads/ophi-rp-29a.pdf?0a8fd7ossietzky, 2014.http://www.let.rug.nl/~heeringa/statistics/stat03_201 3/lect17.pdf
African Journal of Science and Research, 2015,(3)7:15-19 19 11)Prados de la Escosura, L. (2014), World Human Development: 1870 2007. Review of Income and Wealth. doi: 10.1111/roiw.12104 12)Schiffman, S.S., Reynolds, M.L., Youg, F.W.(1981). Introduction to multidimensional scaling: theory methods, andapplications. New York: Acadmic Press. 13)Sturrock, K., & Rocha, J. (2000). A multidimensional scaling stress evaluation table. Field methods, 12(1), 49-60.UNCTAD,(2012) http://unctad.org/en /Publication slibrary/aldcafrica2012_embargo_en.pdf UNDP, (2006) http://www.undp.org/content/undp/en/home/librarypage/c orporate/undp_in_action_2006.html 14)UNDP, (2013) Human Development Index (HDI) - 2012 Rankings, Retrieved 14 January, 2014 from http://hdr.undp.org/en/statistics/ 15)UNDP, (2013) Human Development Report 2013, Technical Notes, Retrieved 28 November, 2013 from http://hdr.undp.org/sites/default/files/hdr_2013_en_techn otes.pdf 16)Wilkinson L. 2002. Multidimensional scaling. In Systat 10.2 Statistics II. Systat Software: Richmond, CA; 119 145. 17)Young, F. W., Takane, Y., & Lewyckyj, R. (1978). ALSCAL: A nonmetric multidimensional scaling program with several individual-differences options. Behavior Research Methods, 10(3), 451-453. 18)Zhang Z, Takane Y., 2014. http://takane.brinkster.net/yoshio/c045.pdf Appendix A - Data Set MYS GDP LE EYS HDI Algeria 13,6 7418 73,4 7,6 0,71 Angola 10,2 4812 51,5 4,7 0,51 Benin 9,4 1439 56,5 3,2 0,44 Botswana 11,8 13102 53 8,9 0,63 Burkina 6,9 1202 55,9 1,3 0,34 Burundi 11,3 544 50,9 2,7 0,36 Cameroon 10,9 2114 52,1 5,9 0,5 Cape Ver 12,7 3609 74,3 3,5 0,59 Central 6,8 722 49,1 3,5 0,35 Chad 7,4 1258 49,9 1,5 0,34 Comoros 10,2 986 61,5 2,8 0,43 Congo_D 8,5 319 48,7 3,5 0,3 Côte d'i 6,5 1593 56 4,2 0,43 Djibouti 5,7 2350 58,3 3,8 0,45 Egypt 12,1 5401 73,5 6,4 0,66 Equatori 7,9 21715 51,4 5,4 0,55 Eritrea 4,6 531 62 3,4 0,35 Ethiopia 8,7 1017 59,7 2,2 0,4 Gabon 13 12521 63,1 7,5 0,68 Gambia 8,7 1731 58,8 2,8 0,44 Ghana 11,4 1684 64,6 7 0,56 Guinea 8,8 941 54,5 1,6 0,36 Guinea-B 9,5 1042 48,6 2,3 0,36 Kenya 11,1 1541 57,7 7 0,52 Lesotho 9,6 1879 48,7 5,9 0,46 Liberia 10,5 480 57,3 3,9 0,39 Libya 16,2 13765 75 7,3 0,77 Madagasc 10,4 828 66,9 5,2 0,48 Malawi 10,4 774 54,8 4,2 0,42 Mali 7,5 853 51,9 2 0,34 Mauritan 8,1 2174 58,9 3,7 0,47 Mauritiu 13,6 13300 73,5 7,2 0,74 Morocco 10,4 4384 72,4 4,4 0,59 Mozambiq 9,2 906 50,7 1,2 0,33 Namibia 11,3 5973 62,6 6,2 0,61 Niger 4,9 701 55,1 1,4 0,3 Nigeria 9 2102 52,3 5,2 0,47 Rwanda 10,9 1147 55,7 3,3 0,43 Sao Tome 10,8 1864 64,9 4,7 0,53 Senegal 8,2 1653 59,6 4,5 0,47 Seychell 14,3 22615 73,8 9,4 0,81 Sierra L 7,3 881 48,1 3,3 0,36 South Af 13,1 9594 53,4 8,5 0,63 Sudan 4,5 1848 61,8 3,1 0,41 Swazilan 10,7 5104 48,9 7,1 0,54 Tanzania 9,1 1383 58,9 5,1 0,48 Togo 10,6 928 57,5 5,3 0,46 Tunisia 14,5 8103 74,7 6,5 0,71 Uganda 11,1 1168 54,5 4,7 0,46 Zambia 8,5 1358 49,4 6,7 0,45