Multivariate Analysis for Social Scientists
A.Y. 2024/2025
Learning objectives
The objective of the course is to introduce students to the logic of quantitative statistical reasoning in social and political sciences. Students will be presented with the main statistical techniques for data analysis used in social sciences, so that they will be able to independently assess and conduct quantitative research.
By the end of the course, students will be equipped with the necessary skills to:
- understand the assumptions underlying the main statistical techniques used in the analysis of social and political phenomena;
- perform descriptive and inferential multivariate analyses on R;
- elaborate a research design for answering a research question with empirical data, applying the statistical techniques learned in this course.
The program is designed to be flexible and can be adjusted if needed, based on the starting level of the students.
In the first part of the course students will be introduced to key concepts and processes involved in designing a research project in social sciences, including formulating a research question and developing hypotheses, and selecting an appropriate data set. This will be followed by a review of univariate and bivariate analyses, OLS regression and its assumptions, and how to deal with deviations from such assumptions. The students will then be introduced to other analytical tools for quantitative analysis, such as non-linear regression functions, logit and probit regressions, and limited dependent variable models. More advanced topics such as time-series and panel-data analyses can be covered upon collective agreement. Students will also learn how to use the statistical software R to organize and analyze data. Lectures are coordinated with computer lab instruction in data analysis.
In the second part of the course, students will be required to elaborate a research design using a real political or social science dataset, and apply the concepts they have learnt to address a research question. Great emphasis will be placed on the formulation of hypotheses and on the use of data to test such hypotheses. Lectures will be based on hands-on material and will provide interactive learning experiences.
By the end of the course, students will be equipped with the necessary skills to:
- understand the assumptions underlying the main statistical techniques used in the analysis of social and political phenomena;
- perform descriptive and inferential multivariate analyses on R;
- elaborate a research design for answering a research question with empirical data, applying the statistical techniques learned in this course.
The program is designed to be flexible and can be adjusted if needed, based on the starting level of the students.
In the first part of the course students will be introduced to key concepts and processes involved in designing a research project in social sciences, including formulating a research question and developing hypotheses, and selecting an appropriate data set. This will be followed by a review of univariate and bivariate analyses, OLS regression and its assumptions, and how to deal with deviations from such assumptions. The students will then be introduced to other analytical tools for quantitative analysis, such as non-linear regression functions, logit and probit regressions, and limited dependent variable models. More advanced topics such as time-series and panel-data analyses can be covered upon collective agreement. Students will also learn how to use the statistical software R to organize and analyze data. Lectures are coordinated with computer lab instruction in data analysis.
In the second part of the course, students will be required to elaborate a research design using a real political or social science dataset, and apply the concepts they have learnt to address a research question. Great emphasis will be placed on the formulation of hypotheses and on the use of data to test such hypotheses. Lectures will be based on hands-on material and will provide interactive learning experiences.
Expected learning outcomes
The course will prepare students to:
- perform descriptive and inferential multivariate analyses using R, including multiple regression models, non-linear regression functions, limited dependent variables, and time-series analysis;
- understand and discuss the underlying assumptions of common statistical techniques in social and political science;
- develop a research design to study social and political phenomena, including defining an original research question, creating a research design, formulating hypotheses, selecting a suitable dataset, conducting statistical analysis, interpreting results, and discussing limitations;
- present their research findings through a public presentation.
- perform descriptive and inferential multivariate analyses using R, including multiple regression models, non-linear regression functions, limited dependent variables, and time-series analysis;
- understand and discuss the underlying assumptions of common statistical techniques in social and political science;
- develop a research design to study social and political phenomena, including defining an original research question, creating a research design, formulating hypotheses, selecting a suitable dataset, conducting statistical analysis, interpreting results, and discussing limitations;
- present their research findings through a public presentation.
Lesson period: Third trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Third trimester
Course syllabus
The course program is structured to provide a comprehensive foundation in multivariate statistical methods tailored to the needs of research in social and political sciences.
1. Introduction to Creating a Robust Research Design: The course begins with an overview of effective research design principles, focusing on how to develop rigorous, valid studies that address key research questions in social and political contexts.
2. Statistical Inference and Significance: Students will explore the fundamentals of statistical inference, including hypothesis testing, p-values, and confidence intervals, laying the groundwork for accurate data interpretation.
3. Monte Carlo Simulations and Statistical Distributions: This module introduces Monte Carlo simulations as a tool for understanding statistical distributions and assessing model reliability, with hands-on exercises to deepen conceptual understanding.
4. OLS Regression for Description and Prediction: Ordinary Least Squares (OLS) regression will be introduced as a method for both describing relationships between variables and making predictions, emphasizing model assumptions and diagnostic techniques.
5. OLS Regression for Causal Inference: Building on previous sessions, students will learn how to apply OLS regression in the context of causal inference, discussing limitations and alternative approaches for identifying causal relationships.
6. Dealing with Categorical Predictors: This session will cover the integration of categorical predictors into regression models, focusing on dummy coding and interpretation of coefficients to understand group differences.
7. Interactive Relationships: Students will learn how to model and interpret interaction effects, examining how the relationship between predictors and outcomes may vary across different levels of other variables.
8. Generalized Linear Models (Logit, Poisson, Beta): Moving beyond linear models, this module introduces Generalized Linear Models to handle non-normally distributed outcomes, with applications in logistic regression, count data models, and models for bounded variables.
9. Hierarchical and Longitudinal Data: The course concludes with techniques for analyzing data with complex structures, such as nested (hierarchical) data and repeated measures (longitudinal) data, allowing students to account for dependencies in their data.
Each topic will combine theoretical instruction with applied exercises, ensuring students develop both an understanding of the methods and the skills to implement them in their own research.
1. Introduction to Creating a Robust Research Design: The course begins with an overview of effective research design principles, focusing on how to develop rigorous, valid studies that address key research questions in social and political contexts.
2. Statistical Inference and Significance: Students will explore the fundamentals of statistical inference, including hypothesis testing, p-values, and confidence intervals, laying the groundwork for accurate data interpretation.
3. Monte Carlo Simulations and Statistical Distributions: This module introduces Monte Carlo simulations as a tool for understanding statistical distributions and assessing model reliability, with hands-on exercises to deepen conceptual understanding.
4. OLS Regression for Description and Prediction: Ordinary Least Squares (OLS) regression will be introduced as a method for both describing relationships between variables and making predictions, emphasizing model assumptions and diagnostic techniques.
5. OLS Regression for Causal Inference: Building on previous sessions, students will learn how to apply OLS regression in the context of causal inference, discussing limitations and alternative approaches for identifying causal relationships.
6. Dealing with Categorical Predictors: This session will cover the integration of categorical predictors into regression models, focusing on dummy coding and interpretation of coefficients to understand group differences.
7. Interactive Relationships: Students will learn how to model and interpret interaction effects, examining how the relationship between predictors and outcomes may vary across different levels of other variables.
8. Generalized Linear Models (Logit, Poisson, Beta): Moving beyond linear models, this module introduces Generalized Linear Models to handle non-normally distributed outcomes, with applications in logistic regression, count data models, and models for bounded variables.
9. Hierarchical and Longitudinal Data: The course concludes with techniques for analyzing data with complex structures, such as nested (hierarchical) data and repeated measures (longitudinal) data, allowing students to account for dependencies in their data.
Each topic will combine theoretical instruction with applied exercises, ensuring students develop both an understanding of the methods and the skills to implement them in their own research.
Prerequisites for admission
An intrinsic motivation to learn statistics is the only hard requirement for this course. Passive, listening-only, and credit-oriented attendance styles are discouraged since they undermine effective and durable learning. Some basic statistics and programming skills (e.g., one previous course in statistics) are recommended but not required in the presence of solid motivation to learn. Some basic R coding experience is also recommended to reduce the overall workload. A basic understanding of introductory statistical and mathematical notions is recommended (having attended the "Data Analysis" course will suffice to this end).
Teaching methods
The teaching methods for this Multivariate Statistics course are grounded in active, student-centered learning and designed to build a collaborative, supportive classroom community. The course emphasizes problem-based learning and hands-on engagement, with students working through real-world datasets and applying statistical techniques directly. Activities foster a collaborative and supportive learning environment, and include: live coding sessions, group problem-solving, and peer discussions, allowing students to learn by doing and to support each other in mastering complex concepts. Feedback is continuous and formative, incorporating regular check-ins, self-assessment, and peer review, so students can track their progress and build confidence. Students will work both individually and in small groups, fostering a learning environment that values collaboration, accountability, and mutual support, helping students develop not only technical skills but also a sense of belonging and resilience in their learning community.
Teaching Resources
1. Kellstedt P.M., Whitten G.D. (2009-2013). The Fundamentals of Political Science Research (2nd edition). Cambridge University Press.
2. Gelman, Hill and Vehtari (2020). Regression and Other Stories. Cambridge University Press.
2. Gelman, Hill and Vehtari (2020). Regression and Other Stories. Cambridge University Press.
Assessment methods and Criteria
Students attending the classes will be evaluated based on:
1. Active class participation and study of the mandatory readings on the platform Perusall (required to pass);
2. Problem sets assigned in class (1/3 of the grade);
3. A final individual project, which must be submitted either as a replication study or as a working paper (2/3 of the grade).
1. Active class participation and study of the mandatory readings on the platform Perusall (required to pass);
2. Problem sets assigned in class (1/3 of the grade);
3. A final individual project, which must be submitted either as a replication study or as a working paper (2/3 of the grade).
Professor(s)