The course specifies and extends some aspects of the wide class of linear models with special reference to the estimability for multivariate linear models with responses both with normal distribution and with exponential class distribution. The lab sessions, with statistical software (SAS and / or R), allow to apply and develop the statistical methodologies.
To provide a thorough introduction to the large class of linear models using the methods of mathematical statistics.
To formulate and apply appropriate regression modelsfor data analysis, to analyse the data with advanced software, to summarise results of the analysis in a report, including the interpretation of the results and their reliability.
Elements of inferential statistics related to estimability and hypothesis testing, including the likelihood theory, especially in setting of the exponential class models. Theory and applications of multiple linear models.
Classroom lectures.
Exercise sessions, with particular emphasis for analysis of specific statistical software output.
Computer laboratory sessions (about 10 hours), whose aim is to practice the application of the theoretical models learnt during classroom lectures, to describe and predict a phenomenon of interests based on real case studies and data sets. During the lab sessions the student will be able to verify his/her level on understanding of the theory and its application.
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.
Dobson A. J. (2001). An Introduction to Generalized Linear Models 2nd Edition. Chapman and Hall. Rogantin M.P. (2010). Modelli lineari generali e generalizzati. Available here. (in Italian)
Ricevimento: By appointment arranged by email fabio.rapallo@unige.it
Ricevimento: By appointment arranged by email at the adress sommriva@dima.unige.it
FABIO RAPALLO (President)
EVA RICCOMAGNO
SARA SOMMARIVA (President Substitute)
The timetable for this course is available here: Portale EasyAcademy
Written exam: calculating exercices and interpretation of parts of SAS or R output. The mark of each single question and the available time (usually three hours) are on the exam paper.
Oral exam: including discussion of lab exercises.
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.
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.
