THE EVALUATION OF THE DEVELOPMENT AGENCY REGIONS IN TURKEY IN TERMS OF SOME SOCIOECONOMIC INDICATOR WITH FACTOR ANALYSES

The actual aim of this paper is to update the periodic studies on defining social-economic development levels of cities in Turkey according to established development agencies. It is believed that considering the development agencies as a one administrative authority would define levels of developments of regions better than considering the cities one by one as an individual. For doing this total values of development agencies of considered regions are found in the manner of their leading socioeconomic indicators and then development agencies regions will be interpreted by using Factor Analysis..


Introduction
Statistical Region Units Classification (SRUC) is defined in Turkey according to the criterion of NUTS which is EU regional classification method and it is put into practice in 2002.SRUC aims making analyses of socioeconomic of regions and generating comparable data with the European United (EU) for reduction of difference development among regions.SRUC consists of three levels.Firstly, in conformity with governmental structure 81 cities are defined as regional units in level 3. 26 regions are defined as region units in level 2 by considering population with forming a group of cities which are similar in terms of economic, social, cultural and geographic manners.According to the same criteria, 12 regions are defined as region units in level 1 with forming a group of 26 regions (Url-1).
In 2006, the development agencies were established depending on State Planning Organization within adjustment laws to the European Union.There are 26 development agencies at present day and each of them corresponds to 26 statistical regions in level 2. These development agencies aim to accelerate regional development.
The actual aim of this paper is to update the periodic studies on defining social-economic development levels of cities in Turkey according to established development agencies.It is believed that considering the development agencies as a one administrative authority would define levels of developments of regions better than considering the cities one by one as an individual.For doing this total values of development agencies of considered regions are found in the manner of their leading socioeconomic indicators and then development agencies regions will be interpreted by using Factor Analysis.

Methods
One of multivariate statistical analysis methods, factor analysis, is used in this study.In factor analysis, it is represented that the variables  1 ,  2 , … ,   as linear combinations of a few random variables  1 ,  2 , … ,   ( < ) called factors.The factors are underlying constructs or latent variables that generate the x's.Like the original variables, the factors vary from individual to individual; but unlike the variables, the factors cannot be measured or observed.If the original variables  1 ,  2 , … ,   are at least moderately correlated, the basic dimensionality of the system is

Alphanumeric Journal
The Journal of Operations Research, Statistics, Econometrics and Management Information Systems ISSN 2148-2225 httt://www.alphanumericjournal.com/ less than p.The goal of factor analysis is to reduce the redundancy among the variables by using a smaller number of factors (Rencher, 2002).
In factor analysis both the standardized variables and the original variables can be used. () and  () are defined as the original data matrix and standardized data matrix, respectively.It is benefited from covariance matrix when original data matrix (X) is used in analysis but the correlation matrix should be employed when standardized data matrix (Z) is used.These cases might give strongly different results.Measure unit is the most important criterion on the selecting the matrix type.If the measure units and variances of the variables are close enough, covariance matrix is used; otherwise correlation matrix is used (Tatlıdil, 2002).
The model of factor analysis with Z () which is derived from X () original data matrix is denoted as; Where   : Factor loading of  ℎ the variable on  ℎ factor   :  ℎ Common factor   : Specific factor   : Coefficient concerning specific factor.This model is also defined as in matrix notation;  =  +  (2) where Z: Standardized data matrix () A: Factor loadings matrix () F: Factor matrix () U: Specific factor matrix () B: Diagonal coefficients matrix ().The actual aim of analysis is to obtain the  = (  ) matrix (Tatlıdil, 2002).
It is known that the variance of variable   in ( 1) is 1.The proportion which is explained by factors of this variance is called as communality and equals to sum of squares of factor loadings related to the variable.The proportion which cannot be explained by factors of this variance is named as specific variance and denoted as   2 .Thus equality (3) can be written in the following form: (3) where ℎ  2 ; Communality   2 ; Specific variance In factor analysis one of the important issues is to determine the proper numbers of factors.There are many various criteria in this subject.
The Criterion of Kaiser: The number of eigenvalues which are higher than 1 of correlation matrix is regarded as numbers of factors.This criterion is used commonly in many fields.
Catell Scree Test (Scree Plot): In this method, catell scree plot is drawn so that the number of component (factor) as 1,2,…,p are in the x-axis and eigenvalue are in the y axis.This plot shows decreasing eigenvalue while the numbers of component (factor) increase.In the plot, the number of component reflecting of point which slope loses is regarded as numbers of factors.
The Criterion of Explained Variance: When the total variance which is explained by eigenvalues is at least %80, the number of eigenvalues is defined as numbers of factors.Some references determine that this rate must be at least 2/3 (%67).
The criterion of Joliffe: The number of the eigenvalues which are 0.70 or greater than 0.70 is regarded as numbers of factors (Özdamar, 2004).
Finally, factor scores can be obtained.Factor scores are the values of estimation of each unit according to common factor structures.In each factor structure (for  1 ,  2 , … ,   ) all variables (     ,  = 1,2, … , ) take part with different weights.While some of these variables play a significant role to define a factor, others don't.Common factor scores of all variables can be calculated by using factor loadings according to factor structure.The factor scores of  − ℎ unit are denoted as: = (΄) −1 ΄   ,  = 1,2, … , .

Application
For the purpose of evaluating the development differences among the regions, some of the socioeconomic indicators of the cities of which take part in Development Agencies are used.The development agency regions are evaluated by applying factor analysis, after the values of considered indicators for each of development agencies is calculated.In this application 19 variables are used and these are shown in Table 2. Factor loadings which shown in Table 2 have an important cognitive content.Each column expresses weight of each variable in factors.On the other hand, each row expresses the relation of each variable with each factor.
Note that, the first 9 variables concentrate on 1th factor, second 8 variables on 2th factor and the rest of variables on 3th factor.
First factor is called as "socioeconomic development factor resting on the power of financial" by regarding the content of variables having high factor loading.Similarly, second factor is called as "the power factor of population and employment" and third factor is called as "the power factor of business".
Factor analysis assumes that the correlations among the variables are caused by common factors.Moreover a big part of correlations among variables emerges due to impact of only one factor.This factor is called as "general causal factor" in literature (Albayrak, 2003).In this survey, it is assumed that there is a general causal factor which effects to all indicators and causes the interaction of indicators.To sum up, general causal factor is the levels of socioeconomic development of regions.
From this point of view, 1st factor which has the greatest eigenvalue and the rate of variance explaining is taken as general causal factor.The factor scores which calculated according to first factor are considered as socioeconomic development index of regions and regions are sorted according to the value of index.Results are shown in Table 3.

Conclusion
In the result of study, the most developed regions are TR10 (İstanbul), TR51 (Ankara), TR31 (İzmir), TR42 (Kocaeli, Sakarya, Düzce, Bolu, Yalova), TR41 (Bursa, Eskişehir, Bilecik), respectively.The values of socioeconomic development index are obtained as negative except these five most developed regions.Contrary to common belief, the region of TRC3 (Mardin, Batman, Şırnak, Siirt) is 10th and the region of TRC2 (Şanlıurfa, Diyarbakır) is 11th.Thus, these regions take part in the first %50.It is believed that this case is caused with the investments made to regions in the last years.The last region is also TR81 (Zonguldak, Karabük, Bartın).As the aim of this study, some interesting results gained.When the 19 variables and methodology used in sorting of regions are applied for 81 cities, different results are occurred.These results are given in Table 4.For example; Kayseri is 14th in the ranking of socioeconomic development according to cities and it take part in the first %20.But, the region of TR72 (Kayseri, Sivas, Yozgat) is 15th in the ranking of socioeconomic development according to regions and it take part in the first %60.As a result, if the socioeconomic development is only examined according to cities, fallacious results can be obtained for the establishments which aim regional development.
In its the last study the Ministry of Development has investigated development of regions (Url-2).In this study any indicator value of region is the weighted arithmetic mean of the indicator values of the cities in the region.The populations of cities are used as weight.However, it is known that this method does not give true value of regions for some variables.
The Development Agencies deal with aims which strive to develop regions and reduce of development difference among regions.In the future, in the socioeconomic development index studies, it is considered that the socioeconomic development of regions must be also researched besides that of cities

Table 3 .
The ranking of socioeconomic development of regions