OVERVIEW

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.

AIMS AND CONTENT

LEARNING OUTCOMES

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.

AIMS AND LEARNING OUTCOMES

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.

By participating in the planned group activities at the end of the course the student will have acquired the following basic skills

• alphabetical-functional (group writing up and individual precentation of group work)

PREREQUISITES

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.

TEACHING METHODS

Classroom lectures.

Exercise sessions, with particular emphasis for analysis of specific statistical software output.

Computer laboratory sessions, 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.

SYLLABUS/CONTENT

Complements of Mathematical Statistics: Methods to evaluate estimators: theorems of Rao-Blackwell and Lehmann-Scheffé. UMVU estimators. Expected Fisher information, Cramer-Rao inequality and efficient estimators. Statistical hypothesis testing: theorem of Neyman-Pearson for simple hypothesis, likelihood ratio test.

Linear models: 

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. Available here. (in Italian)

TEACHERS AND EXAM BOARD

Exam Board

FABIO RAPALLO (President)

FRANCESCO PORRO

EVA RICCOMAGNO (President Substitute)

SARA SOMMARIVA (President Substitute)

LESSONS

LESSONS START

All class schedules are posted on the EasyAcademy portal.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

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.

ASSESSMENT METHODS

The written test evaluates the understanding of the methodologies and their applications and the interpretation of analysis done with statistical software.

The oral exam evaluates the exhibition skills, the understanding and reworking the theoretical aspects of the subject. The course work done during the lab sessions might be subject of the oral exam (thus bring with you at the exams that course work).

Exam schedule

FURTHER INFORMATION

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.