Budget Education and Management as a Necessity for Well-Being and Financial Stability: Cluster & MDS Analysis

From antiquity to modernization, the budget is portrayed as one of the main factors in economic and social life. This paper analyzes the relationship between education and budget management as a necessity for well-being and financial stability. This shows that the use of knowledge during the budget cycle management depends on the education and combination of many factors coming from the environment where the individual or family operates. Here it is explained how Cluster and MDS analysis in interaction with other statistical tests explain the similarities or the differences between the observation groups from Kosovo, Western Balkan countries and European Countries (KO & EU & WBC), related to emergency funds, saving, registration of transactions of revenues or expenditures, financial decision-making, control and budgetary practices. The research is argued from empirical findings giving a new approach through detailed recommendations for variables of observation groups on the personal budget.


Introduction
The field of personal finance, including planning, consulting and financial importance, is a new and very important profession for the country's economy and financial stability (Warschauer, T, 2002). Previous studies have shown that individuals are not very prepared for these new loads and they often manage their finances poorly. In this case, researchers are doing more and more research related to personal budget management, in order to identify the best methods to help increase the financial well-being of society (Soyeon Sh. & Xiao J. & Barber B. & Lyons A., 2009). The same contribution was made by the authors (Hilgert, M. A., Hogarth, J. M., & Beverly, S. G., 2003) where according to them, financial education is important not only for individuals or individual families but also for society as a whole. While the importance for education and financial management continues to increase according to (Joo S., 2008), the situation, attitudes and financial behavior, cannot be evaluated to the same extent. The paper describes the necessity of financial-budgetary education and management for the sustainability of financial stability and the well-being of society in cooperation with other environmental factors. The elaboration of the empirical model was done through two econometric-statistical analyzes. First, based on study variables through Cluster analysis, the classification of surveillance groups (KO&EU&WBC) has been done, in order to see which groups in which variables have more knowledge and in which they should be improved. Second, the findings from the Cluster analysis are elaborated in the multidimensional measurement analysis to provide concrete recommendations through the S matrix for similarities and differences between states and variables. Finally, as stated in the abstract, the combination of these two analyzes through a new approach offers some notable features related to education and budget management, including the fact that financial stability tends to be stable for individuals who have greater education or financial awareness for the budget cycle unlike the other group.

The Purpose of the Research
The purpose of this research is to provide new valuable to education and budget management as a necessity of well-being and financial stability. Where after a period of 1-2 years with same observation, the research will be done again to see if the analysis and recommendations have influenced the improvement or not. Another purpose is to understand how important financial education is to respondents, in which variables are the best or not, in which variables are interrelated and is there a difference between the groups in most variables.

Scope of the Study and the Collection of Data
The research was conducted through questionnaires with respondents from Kosovo's cities, Western Balkan countries and European countries and beyond (18 states). The questionnaire focus was based on previous research related to the two methods involved, based on Likert measurements which are divided into the general question's session and the questions of education and management of the budget. After data is collected it is used to figure out the methods and tests that suits the research.

Methods
The Cluster Analysis (k-means) and the multidimensional measurement analysis (MSD-Alscal) methods, are used for making connections with the tests or methods that are suitable for these two analyzes and research as (Ch-square, Anova, Crosstab, Principal Component Analysis) the research was conducted with all respondents. So, in order for the research to be as important as possible, we first rely on the theory of these analyzes. Cluster analysis is a statistical method with lot of variables which makes classification of data according to similarities, (Hastie, T & Tibshirani, R & Friedman J, 2017), according to groups algorithms (Yuan, Ch & Yang, H, 2019), as well as according to maximum expectations (Ankerst, M. et Al, 1999).This analysis fits with each field of research (Morissette, L & Chartier, L, 2013). Going back to the idea of (Steinhaus, H, 1957) the term "k-means" was first used by (MacQueen, 1967). The techniques they have used in the model are MacQueen algorithm and Hartigan & Wong algorithm, in which case the solution of algorithm depends on the characteristics of data as well as sample size, number of variables etc. Jain, Duin & Mao even suggest trying some algorithms, to gain the best possible understanding of the database (Lloyd, 1982).
A Cluster analysis is efficient and effective if it involves as few groups as possible and should be statistically important (Sig.000). All respondents and variables are divided into three groups (k=3), as (KO-Kosovo, EU-European countries and beyond, WBC-Western Balkan countries), the closer the groups are to each other, the more similar they are considered. To calculate the similarities between these groups is used the distance Euclidian: Where (c) is the center of the group, (x) presents the comparison of groups (KO&EU&WCB), (i or c) is the dimension(x), and (k) is the total number of dimensions. (n=125-3=122/ 2.47435, means 3observations =2.47.
Square distance Euclidian for model is: Also, in k-means is used Manhatan distance: or maximum distance between vector attributes: Algorithm (k-means) represents minimizing the amounts of variances within the groups (n=3) through equation (n i ) is the number of cases included in group (k) and ∑ ni k 1 minimizing variances (125R).
Mathematically k-means analysis is a model that is evaluated through maximum probabilities. Equation for research of budget education and management: C= [c, c 2, … . c n, ] ∈ R d (10) Equation nr. (10) helps to minimize and solve the problem of budget management for three groups.
Equation nr. (11) is the discrete distribution in research.
Represents the continuous distribution to the model, p(x) is the probability density function and (d) is the distance function between cases ns variables.
These steps are included when applying the Cluster analysis: solution of number of groups (n), matric solution that will be used, selecting the method for finding the center of the initial groups, determining the centers of the initial groups C( ), metric threshold (groups, cases): a) For i <= nb cases (respondents for three observations), assigning the closest group, b)a repeated of group centers until the center of group not to be changed within tolerance criterion. Algorithm of budget education and management seeks to divide data into optimal amounts within errors (SEE)groups through the equation: If the sum of (SSE2) for all variables is (i ≠ 1) smaller than current one (SSE1), than the data belongs to this group For evaluation within research group(cluster), is used the Dunn index (1979) through equation: So, ( , , ), is the distance between centers of the groups, which can be calculated with any of the equations presented before and ( ) is the measure of the internal variation of groupings. The highest Dann index, says that the solution is important, it means the greater distance value, the closer the groups are to each other. Linear combination of d-dimensional distribution of Gauss according to group centers is found through logarithm equation This algorithm was first explained by Dempster, Laird & Rubin (1977), who aims to minimize.
Where ( | ), is probabilityod (x i ) (cases), taking into consideration thus it ingenerated by a Gaussian distribution that has (c j ), as a center group, and p(c j ), is the preliminary probability of this research center. The other way of calculating is also through Bayes rules Implementation of Anova (ch-square, crosstab, sub-groups through Tukey and Bonferroni) help the model, to see which groups are different from each other to verify or not hypothesis. During the use of Cluster analysis controls are made so that the results to be important, k=3 to the model shows that group number 1 is located between the two groups. K-means is closely related to non-parametric hypothesis tests (Brian, K & Michael J, 2012). To give details recomamendations to the Cluster analysis model for the cases ans variables help us multidimensional measurement Analysis (MDS) which is very useful statstical method for detecting relationshpis and distance between cases, with a configuration of pints drawn in an abstract Kartezian space. (Mead, A, 1992). The analysis algorithm places each object in the n-dimensional space, in order to keep the distance between the variables of education and budget management as best as possible. For N = 1, 2 and 3, the resulting points can be visualized in a scatter plot (Borg, I. & Groenen, P, 2005). This analysis is otherwise known as key coordinate analyses or Torgerson-Gower scaling, in which case the input matrix shows the difference between the cases and the variables of this research, showing the differences that have come out from results.
is the distance between the coordinates if (i) and (j), taking into consideration this, we have equation: to find the functions of research distance we use the equation: , are the topics of the matrix for three observations(B), defined in the step number 2 of the algorithm. The matrix of coordinate (x) can be derived from the decomposition of the value of Eigen(B= XX'), while (B) matrix can be calculated from the proximity matrix (D) using the double centers of variables and cases (Wickelmaier, F, 2003). The model of this analysis is to verify the groups (C1, C2 ,C3) has gone through steps as below: 1.
Placing the matrix of the square proximity (2)  Now, X = E 1 2 , where ( )is matrix of (m) for value of vector, and ( ) is the diagonal matrix of(m) Eigen value of (B) for education and management of budget. Or Where, (p: 0 ) and -2 ) controlled exponent for distance. The data which will be analyzed (KO, EU, WCB) or n marked with (M) on which is determined the distance function (dij= the distance between cases, variables (i) and (y) ).Below is the matrix equation in the absence of similarity in this case(D) to find (M) vectors (x 1 ,..., X M ϵR N as ‖x i − x j ‖ ≈ d i,j for i,j ∈ 1, … , M. Otherwise this matrix is known as the Euclidian distance. (Kruskal, J. B & Wish, M., 1978). Direct approach of analysis = ( − 1) 2 = 125(125-1)/2, 100(100-1)/2, 2(2-1)/2. Where (Q), is number of variables, (N) is number of cases. The software for running the procedure is available in many statistical packages. There is an often a choice between matrix and non-matrix MDS (Kruskal, J. B, 1964). The dimensions of budget education and management is (2,2), level of measurement (interval), model scale (Euclidean distance), matrix of data (stress convergence 0.001, minimum stress value 0.005). Tools of selection of model as AIC / BIC, Bayes factors or cross verification to be useful for choosing the dimensioning that balances the model.
Theorem of Pythagoras about right triangle:

Hypotheses
Null and alternative hypotheses which test the validity of the model can be written as follows:

H 0 : There is no difference between the observation groups related with budget education and budget financial management. H A : There is difference between the observation groups related with budget education and budget financial management.
if

-H 0 accepted and rejected H A
The purpose of these hypotheses is to see if there is a difference in any of the observations (C1, C2, C3) in most of variables, especially in education and management variables. So that through differences of groups and recommendations coming out from MDS analysis to help individuals and family economies regarding the personal budget. Sufficient information to make financial budget decisions 2 4 3

Item6
Awareness of the importance of financial assurance 3 5 4 Item7 Proper planning for the budgetary financial future 2 3 3

Item8
Saving money as an assistance after retirement 2 3 4 Item9 Creating an emergency fund to overcome crises or meeting budgetary financial needs for 1 to 12 months, in a case of loss of work or ability to work for a while.

4 3
Item10 Registration of all transactions for budget revenues 2 5 3 Item11 Registration of all transactions for budget expenditures 2 4 3

Item12
Saving and investing is important for better well-being 3 4 4 Item13 The need for a financial advisor 3 3 3

Item14
Budget practice and control 2 4 3 Table 2, presents the final data of the groups regarding education and budgetary financial management as a necessity for welfare and financial stability through three observations in 14 variables. The first survey included respondents from countries of Kosovo (KO), in the second group respondents from European (EU) countries and beyond, and in the third survey are included respondents from Western Balkan countries (WBC). To all three countries (KO&EU&WBC), Item1 emphasize that both genders need to increase self-awareness for budget management, but at the same time both genders can be good budget managers in a case of budget awareness. Item2(KO&WBC) emphasize that age is important for budget management, (EU) emphasize that age it is not important but the budget awareness of the age group. To the Item3the greatest response gave (WBC), which says the profession is important for increasing knowledge about financial management, than is (KO), and in the end (EU) gives low rating that emphasizes that the profession does not have an important role if people have better or weak knowledge and management, this depends on their interest in how much they want to be educated about budget management. Item 4 all three observations have the same opinion that education and management helps to realize and save incomes, it means that welfare and financial stability do not depend on the amount of income but on education and budget management.Item5, the highest value is in (EU) while (WBC & KO) has less information about making financial decisions. Item6, higher value for the importance of financial ansurance has (EU), then to (WBC) and (KO). Item7, better planning for the financial future they do (EU &WBC), but even (KO) is not too far from the first two observations. Item8, regarding savings as assistance after retirement the highest value have the countries of (WBC), then (EU) countries. Item9, the emergency funds in extreme cases are more liked from (EU) countries, than (WBC&KO). Item 10 & 11 for the registration of all transactions for income and expenses (KO) has the lowest average, after (KO) is (WBC) and the highest average has (EU). To item12, more interest have (EU & WBC) but also (KO) it is not too far from them in the interest of savings and investment. Item13, the need for a financial advisor in the three surveys (KO & EU & WBC) has the same average. Item14, practice and smaller budgetary financial control has (KO) and the higher value has (EU). 1 2 = 6.6537.  a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 108.0.

Cluster-Chi Square
b. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 40.5.
c. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 64.8. e. 0 cells (100.0%) have expected frequencies less than 5. The minimum expected cell frequency is 72.7.
f. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 97.0.
Tables 5& 6, present the results according to which there is no linear relationship between respondents of different countries regarding education and management as a necessity for well-being and financial stability at the level of importance Sig.000 (P<.005), this means that education and management are different, but the goal is the same for raising awareness about budget management, and especially for (KO&WBC

MDS-Cluster Analysis
Above were emphasized the characteristics of respondents for (KO&EU&WBC) in the level.005, where the differences between them were emphasized. In this case in order to give recommendations for the three Cluster observations as mentioned in the methodology, is used the analysis for multidimensional measurement for respondents and variables. Measurements were initially made respondents-variables, then measurements between variables. This method helps increase education and improve management in all respondents or beyond. Table 7. MDS-Cluster analysis

Between respondents (cases) Between variables
Young's S-stress formula 1 is used. Young's S-stress formula 1 is used.
Iteration S-stress Improvement Iteration S-stress Improvement  Table 7 shows that k=2 has stopped at iteration 4, because the result has been achieved .00034 in the case between respondents (KO & EU & WBC), while in the case between variables (Item 1-14) iteration has stopped at .00027. Z statistic in both cases are close to zero which means that the choice of these variables is appropriate to give recommendations. The value of the Stress matrix according to the Crusal formula for the respondents is 0.77493 and for variables it is 0.80490, according to these matrices related to education and budget management as a necessity for welfare and financial stability budget management (KO&EU&WBC) explained for 77% and 80%. Respondents who have similarities are (11, 13, 60, 16, 35, 18, 55, and 33). The respondents with the largest differences are (20, 43), also respondents (21,87,38) are in the same group, but far from the general trend. Respondents with code (10, 31) are farther from the ideal point and have very different perceptions. So, from the graph it is seen that respondents with code , shows differences from general trend. According to scatterplot of linear fit, the predicated distances correspond to the true value Z=.77.

Figure 2. Euclidean distance (between variables)
Figure 2, shows that ideal point for all variables (Item 1-14) in the both dimensions (1&2) is y= 1*x+0. From the graph in both dimensions we have these recommendations: 1) in dimension 1 between variables: Item 9,1,13 (in order to create an emergency fund for overcoming crises, both genders need a financial advisor). Item 12,7 (proper planning helps save and invest), Item 14,7,10(located within limits of the variable 14, proper planning is don if respondents have budgetary practice and control the budget by recording budget revenues). Item 5, 6, 11(in order to have well-being and financial stability, respondents must have accessible information for making decision, awareness of financial assurance as well as recording expenses). 2) In the dimension between variables: Item 2,12,7,10(education of age group helps save and invest, proper planning for the future, as well as registration of budget revenue transactions). Item 3, 5(all professions must have sufficient information to make budgetary financial decisions, it means it does not depend on the profession but the desire for budget management information). Item 4,6, 11(respondents from their income must record expenses and increase awareness of budget assurance). General recommendations for all variables and respondents: group 1 (2,3,4 is closer to each other), who emphasizes that income is related to age and profession. Group 2 (Item 13,1) which emphasizes that financial advice is necessary for both genders. Group 3 (Item 9,8,12,7,14,10,5,6,11, where variables 9&11are located a little further from the group), that means that if we do not register and control all transactions costs, we do not have opportunity to create an emergency fund. Distance predictions between variables are close to true distances Z=.80, as well as regression confirms the importance of the model 80.2%.

Conclusion
In this paper a significant difference was observed between the observation groups (KO &EU&WBC), in both analyzes was emphasized that small economies due to the environment in which they operate, have poorer financial stability and lower welfare compared to large economies. Below we look at some of the key findings: .8 very few have understood the importance of financial assurance, item3 = 81.2% of cases to some extent plan properly, item9 = 55.2% of the cases to some extent have funds for emergency, item10&11=55.8% of cases rarely make the expense and income registration, item12 = 59.8% of cases agree that saving and investment is important for better well-being, item13 = 64.8% of cases need financial advice, item14 = 61.2% of cases agree that practice and budget control help financial stability. The distance predictions between the variables are close to the true distances Z = .80 and the regression confirms the importance of the 80.2% model. SeeGraph5,


According to the Euclidean distance, the observation groups for all variables should consider the recommendations SeeGraph5 Graph.4,


As stated earlier in small economies some variables are highly correlated with the environment and other indicators, while other negative variables which depend on the cases if not controlled, can worsen financial stability and well-being in society,


Relationships between specific results from cluster analysis and MDS analysis indices were statistically significant,


This study was analyzed only by the variables mentioned.