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Bachelor 2020/2021

## Statistical Modelling of Social and Economic Processes

Type: Elective course (Economics and Statistics)
Area of studies: Economics
When: 4 year, 3 module
Mode of studies: offline
Language: English
ECTS credits: 3

### Course Syllabus

#### Abstract

Methodology of statistical analysis of social and economic processes is the central part of the course. The main attention is paid to differentiation of the population on income, typology of consumers, economic and innovation development of regions and countries, quality of life. We consider how the processes are going on in real life starting with formulation of the problem and finishing with the identification of the models and the analysis of their possible application. Gathering and preliminary analysis of qualitative and quantitative data is provided according to the nature of model variables. The way of an expert's thinking determines the qualitative type of data as the most preferable one. Singular value decomposition of pairwise comparisons allows creating a quantitative variable for a few objects and using these values as a training sample for index constructing. Any attempt to get the quantitative expert information directly gives us as a matter of fact a set of fuzzy values, and we should use it properly on the base of the fuzzy sets theory. Along with constructing the aggregate indicators to reduce the dimensionality, we consider the models of probability density function in a low dimensional space, and the results of its decomposition may be used for soft and crisp classification. When clustering, we can consider pros and cons of the ordinary “k-means” method and its fuzzy modifications. These and other methods are used for creating the models. All the models should be identified using modern computer software.

#### Learning Objectives

• To get the experience in dealing with problems of statistical practice in creating models of social and economic processes.

#### Expected Learning Outcomes

• Student prepares a data set for the statistical model identification, makes the preliminary data processing and transforms the measurement scales of some features, correctly calculates statistics on the base of data with gaps.
• Student creates aggregate indicators of the base level and construct an hierarchical system of aggregate indicators using the results of expert opinions processing.
• Student creates non-parametric and parametric models of probability density function for homogeneous and heterogeneous populations.
• Student provides soft classification of social and economic objects as an alternative to the traditional crisp one, presents and the results of soft clustering.

#### Course Contents

• information support and the stages of social and economic modelling
Statistical data sources. Data scaling. The problem of missing data. Using expert information for statistical modelling. Fuzzy-set approach to enhance the scale level of measurement.
• Index construction techniques and their applications
Expert data aggregation. Index construction with and without training sample. Expert-statistical technique of index construction. Hierarchical systems of aggregate indicators.
• Statistical models of distributions
Probability density estimation in exploratory data analysis. Bootstrap estimation of probability density function. Parametric approach to mixture and compound density estimation. Multivariate probability density function and its decomposition.
• Crisp and soft clustering of social and economic objects
Types of social and economic structures. Classification based on decomposition of probability density function. Crisp and fuzzy strata borders. "k-means" and "c-means" clustering. Membership function in crisp and fuzzy clustering. Evolution of the socio-economic structure. Class description.

#### Assessment Elements

• First home assignment
• Second home assignment
• Class working
• Final exam
• First home assignment
• Second home assignment
• Class working
• Final exam

#### Interim Assessment

• Interim assessment (3 module)
0.25 * Class working + 0.25 * Final exam + 0.25 * First home assignment + 0.25 * Second home assignment

#### Recommended Core Bibliography

• Denis, D. J. (2016). Applied Univariate, Bivariate, and Multivariate Statistics. Hoboken, New Jersey: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1091881