The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data
Abstract
:1. Introduction and Motivation
2. Overview of Social Cohesion Concepts
- Belonging vs. isolation—which refers to the existence or lack of shared values and a sense of identity,
- Inclusion vs. exclusion—which refers to equal opportunities and citizens’ access to economic institutions and the market,
- Participation vs. non-involvement—which refers to political and social participation at various levels of government, especially the local level,
- Recognition vs. rejection—which refers to respect and tolerance of diversity in a diverse society,
- Legitimacy vs. illegitimacy—which addresses the question of respect for existing social norms and laws, the legitimacy of the main political and social institutions, especially the state, as mediators between different stakeholders.
- basic human needs (nutrition and basic medical care, water and sanitation, shelter housing, personal safety),
- foundations of well-being (access to basic knowledge, access to information and communication, health and wellness, environmental quality),
- opportunity (personal rights, personal freedom and choice, tolerance and inclusion, access to advanced education).
3. Research Methodology
- Select a complex phenomenon that cannot be measured directly. In this study, it was the level of social cohesion.
- Select a set of objects and a set of variables closely related with the complex phenomenon of interest. The study involves measuring characteristics of objects (—object number) described by means of variables —variable number). Collected information comprises classic metric data and three types of interval-valued data (min-max, 1st and 9th deciles, 2nd and 8th deciles). Metric data converted into interval-valued data are arranged in the form of data table (. The three types of interval-valued data min-max, 1st and 9th deciles, 2nd and 8th deciles are arranged in data tables (), (, ().
- Combine the data in the form of a single data table () containing data tables , and .
- Add a pattern and anti-pattern object to the set of objects. Variables of interest can be divided into three types of preference variables: stimulants (where higher values are preferred), destimulants (where lower values are preferred), nominants (where the preferred value lies somewhere within the variable range). Formal definitions of stimulants, destimulants can be found in [43] (p. 48) while nominants are defined in [44] (p. 118). These definitions are also provided in [42]. Owing to the structure of the anti-pattern object nominants need to be converted into stimulants. Coordinates of the pattern object represent the most favourable values of preference variables (maximum values for stimulants and minimum values for destimulants). Coordinates of the anti-pattern object represent the least favourable values (minimum values for stimulants and maximum values for destimulants). In the case of symbolic interval-valued variables, coordinates area calculated separately for the lower and upper value of the interval. After including the pattern and anti-pattern object, the joint data table has the form ().
- Normalise interval-valued variables and arrange the data in the form of a normalised data table (; normalised observation) for symbolic interval-valued variables. The purpose of normalization is to ensure comparability of variables (cf. [45]). This is achieved by removing units from measurement results and standardizing their orders of magnitude. Symbolic interval-valued data require special normalization treatment. The lower and upper bound of the interval of the j-th variable for objects ( objects for 4 types of data, pattern and anti-pattern) are combined into one vector containing observations. This approach makes it possible to apply normalization methods used for classic metric data. Metric data were normalized using the interval_normalization function from the clusterSim package implemented in the R program [46].Normalisation methods can be represented by the following formula (cf. [47]):
- Select a measure of distance for symbolic interval-valued data (see Table 2), calculate distances and arrange into a distance matrix .
- Conduct multidimensional scaling (MDS): for all pairs , where f denotes distance mapping from m-dimensional space into corresponding distances in q-dimensional space ( To enable graphic presentation of results q is set to 2. Distances are unknown. The iterative procedure, implemented in the smacof algorithm, used to find configuration (given q dimensions) and calculate distance matrix , is presented in [50] (pp. 204–205).
- 8.
- In the end, as a result of applying multidimensional scaling, we obtain a two-dimensional data matrix (). Depending on the location of the pattern and anti-pattern object in the two-dimensional scaling space the coordinate system needs to be rotated by an angle of according to the formula:
- —data matrix in a two-dimensional scaling space after rotating the coordinate system by an angle of ,
- —rotation matrix.
- 9.
- Visualise and interpret the results (of multidimensional scaling) in a two-dimensional space. This is done by first joining two points, representing the anti-pattern and pattern, by a straight line to form the so-called set axis in the diagram. Then isoquants of development (curves of equal development) are drawn from the pattern point. Objects located between the isoquants represent a similar level of development. The same level can be achieved by objects located at different points along the same isoquant of development (due to a different configuration of variable values).
- 10.
- Order objects according to the value of the aggregate measure based on the Euclidean distance from the pattern object [43]:
4. Data
5. Results of the Empirical Study
5.1. Results for Metric and Interval-Valued Data
5.2. Comparative Analysis of the Results in the Assessment of Social Cohesion
- 16 provinces of Poland for 4 datasets (metric, min-max, 1st and 9th decile, 2nd and 8th decile) are linearly ordered according to a set of m variables to produce 4 rankings based on aggregate measures (see Table 4).
- For each variable () a distance between each object and the pattern object is calculated according to the formula (the Ichino-Yaguchi distance for one variable):This yields m values of measures
- The general rankings based on the aggregate measures (step 1) are compared with individual rankings based on measures (step 2), separately for each data type using Spearman’s and Kendall’s correlation coefficients.
- For each data type, the median of results obtained in step 3 is calculated. A higher value of the median represents a higher degree of compatibility between rankings based on individual variables and the ranking based on the aggregate measure. The results are displayed in Table 6.
6. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Type | Method | Parameter | |
---|---|---|---|
n1 | Standardisation | ||
n2 | Positional standardisation | ||
n3 | Unitisation | ||
n3a | Positional unitisation | ||
n5 | Normalisation to range | ||
n5a | Positional normalisation to range | ||
n12a | Positional normalisation |
Symbol | Name | Distance Measure |
---|---|---|
U_2_q1 | Ichino-Yaguchi | |
U_2_q2 | Euclidean Ichino-Yaguchi | |
H_q1 | Hausdorff | |
H_q2 | Euclidean Hausdorff |
Dimensions | Variables |
---|---|
Basic human needs | x1—mean gross monthly wage in PLN (Polish new zloty) |
x2—total unemployment rate in % | |
x3—mean useful floor area of a dwelling per inhabitant in m2 | |
x4—average number of persons per room | |
x5—length of the sewerage network in relation to the length of the water supply network in % | |
x6 – number of doctors and dentists per 10,000 population | |
x7—crimes reported (criminal offenses, against life and health, against property) per 10,000 population | |
x8—road accidents per 100,000 population | |
Foundations | x9—users of water treatment services (% of total population) |
of well-being | x10—percentage of all dwellings equipped with central heating |
x11—children enrolled in day-care centres per 1000 children up to the age of 3 | |
x12—children enrolled in nursery schools per 1000 children aged 3–5 | |
x13—students taking obligatory classes of English in primary and intermediate schools (% of all students) | |
x14—members of sports clubs per 1,000 population | |
x15—people participating in cultural events (organised by cultural centres and clubs) per 1000 population | |
x16—area of public greenspace (parks, residential greenspace) per 10,000 population (in ha) | |
x17—length of municipal and district improved hard surface roads per 10,000 population (in km) | |
x18—death rate among persons below the age of 60 | |
Opportunities | x19—dependency ratio (ratio of the dependent and elderly population per 100 working age population) |
—percentage share of women in the labour force | |
x21—percentage share of young adults (up to the age of 25) among registered unemployed | |
x22—percentage share of long-term unemployed (over 12 months) in the population of registered unemployed in % | |
x23—places in stationary social welfare facilities per 10,000 population | |
x24—voter turnout local elections (for municipal authorities and town councils with district rights) in 2018 in % | |
x25—beneficiaries of social assistance at the place of residence (below the means test threshold) per 1000 population |
Province | no | Metric | Rank | d2-8 | Rank | d1-9 | Rank | Min-Max | Rank |
Mazowieckie | 16 | 0.5472 | 1 | 0.4348 | 10 | 0.4400 | 12 | 0.4161 | 13 |
Dolnośląskie | 6 | 0.5229 | 2 | 0.5040 | 5 | 0.5316 | 4 | 0.5641 | 5 |
Śląskie | 2 | 0.5042 | 3 | 0.5410 | 1 | 0.5450 | 3 | 0.5887 | 3 |
Opolskie | 7 | 0.5035 | 4 | 0.5125 | 3 | 0.5283 | 5 | 0.6116 | 1 |
Lubuskie | 3 | 0.4904 | 5 | 0.5204 | 2 | 0.5465 | 2 | 0.6048 | 2 |
Wielkopolskie | 4 | 0.4832 | 6 | 0.4901 | 7 | 0.5177 | 7 | 0.5273 | 6 |
Pomorskie | 9 | 0.4772 | 7 | 0.5113 | 4 | 0.5254 | 6 | 0.5203 | 7 |
Zachodniopomorskie | 5 | 0.4765 | 8 | 0.5034 | 6 | 0.5473 | 1 | 0.5657 | 4 |
Małopolskie | 1 | 0.4546 | 9 | 0.4578 | 8 | 0.4732 | 9 | 0.4413 | 10 |
Łódzkie | 11 | 0.4431 | 10 | 0.4531 | 9 | 0.4684 | 10 | 0.4736 | 8 |
Podlaskie | 15 | 0.4311 | 11 | 0.3786 | 16 | 0.4009 | 15 | 0.3727 | 15 |
Kujawsko-Pomorskie | 8 | 0.4202 | 12 | 0.4121 | 13 | 0.4215 | 13 | 0.3805 | 14 |
Świętokrzyskie | 12 | 0.4117 | 13 | 0.3933 | 14 | 0.3959 | 16 | 0.4268 | 12 |
Lubelskie | 13 | 0.4058 | 14 | 0.4255 | 11 | 0.4529 | 11 | 0.3714 | 16 |
Warmińsko-Mazurskie | 10 | 0.3874 | 15 | 0.3835 | 15 | 0.4010 | 14 | 0.4517 | 9 |
Podkarpackie | 14 | 0.3849 | 16 | 0.4214 | 12 | 0.4746 | 8 | 0.4274 | 11 |
Parameters | |||||||||
Mean | 0.4590 | 0.4589 | 0.4794 | 0.4840 | |||||
Standard deviation | 0.0477 | 0.0518 | 0.0543 | 0.0821 | |||||
Median | 0.4656 | 0.4555 | 0.4739 | 0.4627 | |||||
Median absolute deviation | 0.0568 | 0.0715 | 0.0792 | 0.1088 |
Data | m | d2-8 | d1-9 | mm |
m | 1.000/1.000 | |||
d2-8 | 0.721/0.567 | 1.000/1.000 | ||
d1-9 | 0.629/0.417 | 0.969/0.750 | 1.000/1.000 | |
mm | 0.625/0.450 | 0.896/0.650 | 0.877/0.633 | 1.000/1.000 |
No. | Types of Data | Median Value | |||
---|---|---|---|---|---|
Spearman’s | Rank | Kendall’s | Rank | ||
1 | Metric data | 0.4176 | 3 | 0.2667 | 3 |
2 | Interval-valued (2nd and 8th deciles) | 0.4371 | 1 | 0.3333 | 1 |
3 | Interval-valued (1st and 9th deciles) | 0.4297 | 2 | 0.2833 | 2 |
4 | Interval-valued (min-max) | 0.2676 | 4 | 0.1667 | 4 |
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Walesiak, M.; Dehnel, G. The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data. Sustainability 2020, 12, 7664. https://doi.org/10.3390/su12187664
Walesiak M, Dehnel G. The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data. Sustainability. 2020; 12(18):7664. https://doi.org/10.3390/su12187664
Chicago/Turabian StyleWalesiak, Marek, and Grażyna Dehnel. 2020. "The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data" Sustainability 12, no. 18: 7664. https://doi.org/10.3390/su12187664
APA StyleWalesiak, M., & Dehnel, G. (2020). The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data. Sustainability, 12(18), 7664. https://doi.org/10.3390/su12187664