# GENERALISED LINEAR MODELS

iten
Code
101515
2020/2021
CREDITS
6 credits during the 3nd year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
SECS-S/01
TEACHING LOCATION
GENOVA (Mathematical Statistics and Data Management)
semester
1° Semester
Teaching materials

## 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

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.

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

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)

## TEACHERS AND EXAM BOARD

Exam Board

MARIA PIERA ROGANTIN (President)

MARTA NAI RUSCONE

EVA RICCOMAGNO (President Substitute)

## LESSONS

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.

Class schedule

All class schedules are posted on the EasyAcademy portal.

## 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

Date Time Location Type Notes
21/12/2020 09:00 GENOVA Scritto
21/12/2020 09:00 GENOVA Orale
18/01/2021 09:00 GENOVA Scritto
19/01/2021 09:00 GENOVA Orale
16/02/2021 09:00 GENOVA Scritto
17/02/2021 09:00 GENOVA Orale
09/06/2021 09:00 GENOVA Scritto
09/06/2021 09:00 GENOVA Orale
12/07/2021 09:00 GENOVA Scritto
12/07/2021 09:00 GENOVA Orale
09/09/2021 09:00 GENOVA Scritto
09/09/2021 09:00 GENOVA Orale