OVERVIEW

This course develops the theory of linear and generalized linear models, with a particular focus on methodological aspects. Topics covered include multiple and multivariate regression, as well as generalized linear models for response variables from the exponential family. Applications in the biomedical, engineering, and economic fields are also presented through lab sessions carried out using appropriate statistical software (SAS and/or R).

AIMS AND CONTENT

LEARNING OUTCOMES

To provide a thorough introduction to the large class of linear models using the methods of mathematical statistics.

AIMS AND LEARNING OUTCOMES

The course is structured in two parts:

1. General Linear Models: multiple and multivariate regression, regression for repeated measures.
2. Generalized Linear Models: maximum likelihood estimation, logistic, multinomial, and count regression; log-linear models.

All topics will be accompanied by practical exercises using SAS or R, so that students can complement their theoretical understanding with the ability to perform appropriate statistical analyses in real-world settings and to interpret the outputs of statistical procedures.

Knowledge and understanding: Students are expected to acquire knowledge of the main classes of regression models, to frame these models in general terms (both theoretical and applied), and to understand the underlying mathematical tools.

Applying knowledge and understanding: Students will be able to identify the appropriate analysis technique for applied problems in various contexts. They will also be able to critically assess the results obtained through statistical software.

Making judgments: Students will develop an awareness of the strengths and limitations of the statistical techniques presented, through the analysis of examples and case studies.

Communication skills: Students will learn to use correct statistical terminology for communicating results and describing the techniques used, and they will be able to prepare effective reports to present the outcomes of statistical analyses.

Learning skills: Students will develop adequate learning abilities that will enable them to further explore the subject independently.

PREREQUISITES

Elements of inferential statistics and concepts from mathematical statistics related to estimability and hypothesis testing, including tools from likelihood theory, particularly within the framework of exponential family models. Theory and applications of the multiple linear regression model. Fundamentals of using SAS and R software.

TEACHING METHODS

Classroom lectures to present the theoretical framework and to work through exercises, including the interpretation of results obtained using specific statistical software.

Lab sessions (approximately 10 hours) to apply the statistical methodology presented during the classroom lectures and to define correct statistical models for inference and prediction, using real data. These sessions allow students to assess their understanding of statistical theory and to gain deeper insight into practical applications.

SYLLABUS/CONTENT

General linear models. ANOVA: crossed and nested factors; unbalanced data. Overparametrised models: reparametrization and generalised inverse function: theoretical considerations and practical implications. Multivariate linear regression models and models for repeated measures. 

Generalised linear model. Exponential family. Link function. Models for categorical data (binomial, multinomial and Poisson models). Iterative methods for coefficients’ estimation: Newton-Raphson, scoring. Asymptotic distributions for likelihood based statistics. Statistical hypothesis testing and goodness of fit criteria: deviance, chi-squared. Residuals. Tests and confidence intervals for (subsets of) the models parameters. Odds-ratio and log-odd ratios. Models for ordinal data and contingency tables. 

Lab sessions based on the softwares SAS and R. 

RECOMMENDED READING/BIBLIOGRAPHY

Dobson A. J. (2001). An Introduction to Generalized Linear Models 2nd Edition. Chapman and Hall.
Rogantin M.P. (2010). Modelli lineari generali e generalizzati. Teaching notes available on the AulaWeb page of the course.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Lesson starts on 25 September 2025.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written test and an oral examination.

The written test includes two exercises: one concerning the theoretical aspects of the course, and one more applied which also requires the interpretation of SAS or R output. In order to be admitted to the oral examination, students must achieve at least a borderline pass grade in the written test.

The oral examination consists of one or more questions related to the theoretical part and the lab exercises covered during the course.

ASSESSMENT METHODS

In the written exam, the understanding of notions, calculation skills, and especially the interpretation of SAS or R outputs are assessed.

The laboratory activity is evaluated through the submission of two reports on the topics covered during the exercises. These reports will assess the ability to apply the acquired techniques to real-life situations and the command of the specific language of the discipline.

In the oral exam, the ability to present, understand, and elaborate on the theoretical aspects of the subject are assessed. The evaluations of the written exam and the laboratory work form the basis for determining the overall outcome of the exam.

FURTHER INFORMATION

Students with disabilities or specific learning disorders (DSA) are reminded that in order to request adaptations during the exam, they must follow the instructions described in detail on Aulaweb on the "Lauree in Matematica e SMID" page. Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.