This paper delves into an in-depth exploration of multidimensional statistical analysis techniques aimed at categorizing regions based on their levels of investment attractiveness, while also scrutinizing the evolving regional structures in light of the persistent and adverse efects of the COVID-19 pandemic. Through a comprehensive review of various approaches to assessing investment attractiveness, the study highlights their respective strengths. Notably, the research underscores the underutilization of multidimensional statistical analysis methodologies in the regional grouping context. The authors undertake the task of clustering Ukrainian regions based on their investment attractiveness levels, employing the well-regarded -means method. This analysis extends to the identification of the regions' investment attractiveness structure in both 2019 and 2020, amid the COVID-19 pandemic. Substantiating the validity of their findings, the authors employ the principal component method in conjunction with the quartimax technique to rotate the space of selected factors. Remarkably, the subsequent regional grouping in this transformed principal component space mirrors the outcomes of the cluster analysis method. The research outcomes hold practical value for potential investors, enabling them to pinpoint key investment areas. Furthermore, local self-governing bodies stand to benefit from these findings, gaining insights into specific regions' relative investment attractiveness levels compared to their counterparts, while also uncovering vulnerabilities in distinct activity domains. socio-economic development, regional analysis, investment attractiveness, clustering, -means method, principal component analysis, quartimax method M3E2-MLPEED 2022: The 10th International Conference on Monitoring, Modeling & Management of Emergent Economy, ⋆Extended and revised version of paper [1] presented at the 10th International Conference on Monitoring, Modeling & Management of Emergent Economy.
pandemic⋆
Investment activities are crucial for the sustainable socio-economic development of territories, as they provide the financial basis for enhancing the performance of enterprises, creating new employment opportunities, and improving the quality of life. To achieve these goals, it is necessary to use analytical tools that can support the management of regional development. One of the key components of such tools is economic and mathematical modeling, which can use relevant data to fit models that can provide quantitative and qualitative assessments of the state and dynamics of socio-economic development. One of the applications of such modeling is to evaluate the investment attractiveness of regions, which reflects their potential to attract and retain investors.
However, the investment attractiveness of regions is not static, but rather influenced by
various factors, such as globalization, market competition, and external shocks. In particular,
the COVID-19 pandemic has caused significant structural and technological changes in the
economy [
In this paper, we address the problem of assessing the investment attractiveness of regions and their grouping based on their similarities and diferences. We use multidimensional statistical analysis, a widely used technique in computer science and data science, to reduce the dimensionality of a large set of indicators that measure various aspects of investment attractiveness. We then apply clustering methods to identify groups of regions that share common characteristics and trends in terms of investment attractiveness. We also analyze how the COVID-19 pandemic has afected the regional changes in investment attractiveness and discuss the implications for regional policy and planning.
Assessing the region’s investment attractiveness is essential in developing a strategy for
innovation at regional and national levels. Note that the investment volume isn’t always directly
determined by the high level of investment attractiveness. This is due to many other factors
that determine investor decision-making. In particular, such factors are various indices and
ratings regularly published by international institutions and characterize the business
environment, business conditions, actual investment activities, and the attractiveness of countries
for investment. In particular, it can be used such evaluations like the World Bank Ranking
“Doing Business” [
These ratings provide the necessary information for potential investors on the characteristics of the country’s business environment and possible investment risks. Naturally, countries with high ratings are more attractive regarding return on investment. On the other hand, countries with low ratings may also be attractive to investors, particularly for short-term investments, resulting from competition for coverage of developing countries.
These ratings should be noted that characterize the country’s business environment. At the
same time, investors are usually interested in specific areas, territorial units, markets, sectors
of the economy, and business entities. Such assessments of the investment attractiveness of
certain regions of Ukraine are provided by the State Statistics Service of Ukraine [
The issue of investment attractiveness is also the focus of research. The formation of the theoretical basis for the study of the category of investment attractiveness in the context of its relationship with the investment climate, and investment risks, taking into account current trends in economic development, is reflected in the works by Kaminskyi et al. [16], Stadnyk et al. [17], Korenyuk and Kopil [18], Kyshakevych et al. [19], Godlewska-Majkowska [20], Jac and Vondrackova [21]. Researchers presented a modern understanding of the category of investment attractiveness, its content and essential characteristics, and the impact on the socio-economic development of individual regions and the country as a whole.
An important issue in modeling investment attractiveness is forming an information base for calculating various estimates of the studied characteristics. The solution to such problems is considered by Kyshakevych et al. [19], Jac and Vondrackova [21], Bushynskyi [22], Leshchuk [23], Lagler [24], Swidynska and De Jesus [25]. It should be noted that the results of scholars’ investigations in this field are difered both in the number of indicators and their focus in the context of reflecting certain aspects of investment activities. At the same time, the authors’ positions coincide with the views that the indicators should reflect the economic, financial, and social aspects of regional development.
Modeling the investment attractiveness of regions is mainly based on statistical methods.
Their application is based on quantitatively measurable indicators that reflect social, economic,
environmental, and investment development components. This approach uses regression
models, that presented in papers [
Among the shortcomings of the comprehensive index assessment technology application presented in these investigations, it should be noted that they use a fairly large set of initial indicators. This makes it dificult to identify the significance of their impact on the final result and eliminates the diferentiating ability of the designed composite index. These shortcomings negatively afect the ability to group the set of studied objects due to the high density of values on the composite index scale. Also out of consideration is the definition of the level of investment attractiveness of regions, which complicates the assessment of diferences between regions on the calculated index.
The problems of rating regions can also be solved with the application of multidimensional
statistical analysis technology, that described, in particular, by Tenreiro Machado and Mata
[
At the same time, applying these methods is focused mainly on solving the problem of grouping regions in terms of investment attractiveness. The analysis of structural shifts within the constructed homogeneous groups remains out of the attention of scientists, as well as the comparison of grouping results obtained by diferent techniques.
According to the results of the analysis of publications, it can be concluded that there is significant diversity in approaches to assessing the investment attractiveness of regions. Among the disadvantages, we can note that the calculations are carried out without considering the dynamic and qualitative changes in the environment.
Also, the use of a large number of baseline partial indicators, to some extent, blurs the study’s results and gives only a general description of the socio-economic condition of the region and the characteristics of investment activities.
The significant variety of calculated estimates and the lack of clear conclusions and recommendations for their practical application necessitates the further study of the problem of assessing the investment attractiveness of regions in the context of their grouping by using diferent techniques to solve this problem with the further comparison of grouping results and structural changes within groups.
The solution to these problems has led to the direction of research in this study.
A large number of diferent indicators characterize modern investment processes. This multidimensionality of the description makes it dificult to solve problems of assessing the various characteristics of these processes, particularly the grouping of regions by the level of investment attractiveness. As noted earlier, one way to solve classification problems is using cluster analysis techniques. Unlike combinational grouping, this approach allows you to create groups of similar objects of observation, considering all the features at once. The degree of similarity, in this case, is usually the Euclidean distance between objects in the multidimensional space of primary indicators. One of the cluster analysis methods is the -means method, which belongs to the group of iterative clustering ones.
Consider a brief description of the mathematical model of the -means method [
We need to divide these observations into clusters that do not intersect. At the initial stage, we choose points-objects that will act as centers of clusters. Denote them by 1(0), 2(0), … , (0). The weight of each cluster will initially be equal to one: 1(0) = 1, 2(0) = 1, … , (0) = 1. The index of the corresponding center will be considered the index of the corresponding cluster. Although the selected centers may move to other clusters during the subsequent iterative procedure, the indexing of the clusters will not change.
In the first step, each of the ( − ) objects that are not the clusters’ centers is included in one of the formed clusters. The criterion for such movement is the minimum distance to the cluster’s center. The center of the cluster and its weight are recalculated. For example, for a point +1 with coordinates ( +1,1 ; +1,2 ;…; +1, ) the recalculation is performed according to the formulas: (0) = (0) (0) + +1
, (0) = constructed in such a space.
In matrix form, the model of the method is described by the formula: where is an initial standardized indicators matrix;
– factor loadings matrix; it reflects relations between initial indicators and principal In the case of equality of two or more distances to the centers of clusters, the point-object joins the cluster with a smaller sequence number. Note that in practice, such a situation is unlikely.
The resulting centers and corresponding cluster weights are taken as the initial values of the related characteristics for the next iteration.
All stages of the further iterative process use formulas (1) and (2) and the whole set of initial data 1, 2, ..., . At the same time, the weight of clusters continues to increase.
The objects can also be grouped by expanding them in some new space of latent scales, which reflect the generalizing characteristics. In particular, the principal components method can be Factor loadings matrix is calculated using eigenvalues and appropriate eigenvectors of – (1) (2) (3) (4) (5) (6) components;
– principal components matrix. initial indicators correlation matrix: where – factor loadings matrix; – normalized eigenvectors matrix; Λ – eigenvalues matrix.
The rule obtains the initial indicators correlation matrix: where – correlation matrix; – initial standardized indicators matrix.
The standardization procedure for initial indicators uses a formula: where – initial standardized indicators values; = ⋅ , = ⋅ Λ
(−1), = ⋅ − 1
, = − ̄ – initial indicators values; ̄ – average sample value of the indicator ; – sample standard deviation of the indicator ; = 1..; = 1...
The formula obtains the principal components matrix: = ⋅ ⋅ Λ −1.
(7) This matrix contains the coordinates of objects under study in a principal components space.
Not all the principal components are selected for practical application, but only the most essential part in explaining the variance of the initial indicators (information contained in the initial indicators). Given that the eigenvalues of the correlation matrix are considered to be ordered in descending their values in the calculation procedure, the weight of each subsequent principal component is reduced. Usually, the first two principal components are suficient to achieve an “acceptable” level of explanation of the information contained in the set of initial indicators, at least 70 %.
Meaningful interpretation of the selected principal components (search for names for them) is carried out by considering the absolute values of the respective factor loads. The initial indicators that will be used to interpret the appropriate principal component include those for which the factor loadings absolute value between them and the corresponding principal component is not less than 0.75. The factor load reflects the correlation between the principal component and the related indicator. To improve the procedure of interpretation of the principal components by the problem’s content, the constructed factor space is rotated with a corresponding change in both factor loadings and values of the principal components. The result is a “simple structure” space where the principal components are closely related to some initial indicators and weak to others.
Consider the application of cluster analysis of the grouping of Ukraine’s regions by indicators that reflect their investment attractiveness. The choice of the initial indicators set will be made based on the following considerations: • indicators should reflect both the characteristics of investment activities of the region’s business entities and the socio-economic development of the region; • indicators should be comparable by the values for diferent regions; • the indicators must be standardized, i.e., have a sample mean equal to zero and a sample standard deviation equal to one. This procedure is needed because clustering is based on a matrix of diferences between the studied points-regions in the multidimensional space of the initial indicators, which is essentially a matrix of Euclidean distances between them. Therefore, for the objectivity of the calculations, it is necessary to remove the measurement units’ influence on estimates of distances between objects.
Based on the recommendations by Korenyuk and Kopil [18], Kyshakevych et al. [19],
Godlewska-Majkowska [20], Jac and Vondrackova [21], Bushynskyi [22], Leshchuk [23], Lagler
[24], Vartsaba and Leshuk [
We use data for 2019 and 2020 from the materials of the State Statistics Service of Ukraine [55] and the Ministry of Development of Communities and Territories of Ukraine [15] for calculations. Obtained results will also be compared to assess changes in regions’ position in the groups in which the regions are located. To present the region’s names conveniently and briefly, we point out the correspondence between each region’s name and the appropriate code (table 1). Initial data for calculations are written in table 2 and table 3.
Let us cluster Ukraine’s regions according to the selected set of indicators using the -means method. Define the number of clusters for grouping regions as equal to three: a cluster of regions with a high level of investment attractiveness, a cluster of regions with a medium level of investment attractiveness, and a cluster of regions with a low level of investment attractiveness. We make calculations using “Statistica” software. The results of clustering are shown in figure 1 and figure 2. The numbering of clusters, in this case, is determined by the used software arbitrarily. Let us provide a meaningful description of each cluster according to 2019 data.
Code
Cluster number 1 contains 6 regions: Volyn, Donetsk, Zakarpattia, Kyrovohrad, Luhansk and Ternopil. In our opinion, this cluster can be called a group of regions with a low level of investment attractiveness. Note that the regions of this cluster are not industrially developed, which negatively afects their attractiveness for investment. In addition, the efects of the COVID-19 pandemic have had a significant negative impact on the development of these regions. Cluster number 2 contains regions with an average level of investment attractiveness. It is the most complete and consists of 14 points, which is quite natural in compliance with the essence of the division of the typical characteristics. The cluster with a high level of investment attractiveness includes cluster number 3, which includes Dnipro, Kyiv, Zaporizhzhia, and Poltava regions. For these regions, there are high values of the indicators presented in table 2, particularly the volume of foreign direct investment and relatively high employment rate, which allowed to give the cluster just such an interpretation. In addition, these regions have developed industries, which is also reflected in the indicator’s values.
Comparing the cluster’s structure obtained from 2020 data (figure 2), we can conclude that the fullness of clusters has not changed compared to the previous year. This indicates that there have been no significant changes in the investment attractiveness of Ukraine’s regions in 2020. Although several normative acts have been adopted at the legislative level to facilitate attracting investments into Ukraine’s economy, their positive impact has not yet manifested itself. On the other hand, it is possible to state a certain stabilization of indicators of socio-economic development of Ukraine’s regions during the COVID-19 pandemic.
Let us consider the data of application of the principal components method for grouping Ukraine’s regions by the level of investment attractiveness. We create the two-dimensional space of latent indicators obtained by applying this method and project points-regions on this space. To construct latent indicators, we use the quartimax method for rotations of factor space, which will contribute to an adequate representation of points in the new space and the identification of meaningful interpretation of new axes.
Calculations also are performed using Statistica software. The calculations’ results of factor loadings are presented in table 4, and the values of points-objects in the new space – are in table 5. Note that in this case, the degree of explanation of the variance of the initial indicators by selected factors (degree of latent indicators informativeness) is 77 % for 2019 and 79 % for 2020 data. These indicators indicate the suficiency of allocating exactly two principal components as latent indicators for further analysis.
Table 4 analysis allows us to provide such an interpretation of the selected principal components. Component 1 has high factor loadings values for the initial indicators 1 − 6, and low for 8 and 9. Therefore, we can conclude that 1 is an economic component of investment attractiveness, as the corresponding indicators 1 − 6 are characteristics of economic activity. For indicators 8 and 9 there are high values of factor loadings for component 2 and low for 1. Based on the essence of indicators 8 and 9, we can conclude that 2 can be interpreted as a social component of investment attractiveness. For indicator 7, the value of factor loadings for the principal component 1 in 2019 exceeds the corresponding value for component 2, although this excess is insignificant. In 2020, the situation was reversed. Based on the essence of indicator 7, we can conclude that it can characterize both the economic and social components of regional development; that is, the interpretation of the results is not essentially afected by this indicator.
Graphic representations of the regions in the space of the identified principal components according to the data of 2019 and 2020 are respectively presented in figures 3 and 4.
Figure 3 analysis allows us to conclude that we can also identify three clusters of regions. The resulting clusters in terms of content correspond to the formed clusters obtained by the -means method. A similar situation occurs in figure 4. The results of a grouping of regions obtained using the principal components method are identical to those obtained from the clustering method.
However, it is worth noting. Figure 3 shows that cluster number 1 can be divided into at least two smaller clusters, including points C_7 (Zaporizhzhia region) and C_15 (Poltava region) to one of them and points C_3 (Dnipro region ) and C_9 (Kyiv region) to the other. Similarly, points C_7 and C_15 can be allocated from cluster number 2 to a separate cluster. In the third cluster, we can distinguish points C_4 (Donetsk region) and C_11 (Luhansk region), which form two diferent clusters. So, the cluster structure may be more complex and require a more complex interpretation of the results. A similar situation occurs in figure 4.
However, according to the task, our study proceeded from a predetermined number of clusters. And the methods used in the study gave identical results.
Investment activity is always associated with a specific risk. Potential investors need to conduct a comprehensive study of the investment object to reduce the potential risks. One of the approaches is to assess its investment attractiveness. For individual territorial entities, such as regions, it is advisable to determine the quantitative measures of the level of investment attractiveness and group them according to this indicator. This will identify regions with roughly the same investment climate.
Code C_1 C_2 C_3 C_4 C_5 C_6 C_7 C_8 C_9 C_10 C_11 C_12 C_13 C_14 C_15 C_16 C_17 C_18 C_19 C_20 C_21 C_22 C_23 C_24
In this paper, we used the -means method of clustering to divide the regions of Ukraine into relatively homogeneous groups according to the level of investment attractiveness. We used data for 2019 and 2020, which were characterized by the COVID-19 pandemic. We limited ourselves to the selection of three clusters, which were given a meaningful interpretation: the ifrst one is a cluster with regions that have a high level of investment attractiveness, the second cluster contains regions with a medium level of investment attractiveness, and the third cluster includes regions with a low level of investment attractiveness.
Comparing clustering results for selected periods showed that the cluster structure of Ukrainian regions has not changed. To verify the correctness of the obtained grouping of regions, we deployed the regions of Ukraine in the space of latent indicators, which were calculated on the same data set by the method of principal components. A meaningful analysis of factor loads showed that one latent axis of the new space characterizes the economic component of investment attractiveness, and the other is the social component. The results of grouping Ukraine’s regions turned out to be identical to those obtained by the -means method.
We conclude that it would be more appropriate to allocate more clusters, which would provide a more accurate picture of the grouping of regions by the level of investment attractiveness. Such an assessment can be helpful for local governments, as it provides information on the relative level of investment attractiveness of a particular region compared to other territorial units and identifies weaknesses in the areas of activity on which the assessment was based. Such results can be used to create and adjust regional socio-economic development programs, particularly in terms of planning to attract investment into the region’s economy.
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