85160 - Statistical Models and Applications

Learning outcomes

By the end of the course the student learns the basic notions to define statistical models. In particular, the student is able to estimate parameters, test hypothesis about them and build confidence intervals for generalized linear models and for linear mixed models, and to choose the most suitable model for the specific problem at hand.

Course contents

Part I

Statistical Models: introduction

Gaussian linear models:

• definition
• parameter estimation
• hypothesis testing
• model choice and variable selection model
• diagnosis
• extensions

Gaussian linear mixed models

• definition
• fixed and random effects
• variance-covaraince matrix structures
• likelihood inference

Nonparametric regression based on spline functions

Part II

Generalized linear models

• definition: exponential families and link functions
• likelihood inference: estimation and hypothesis testing
• binary regression
• count data regression
• models for nonnegative dependet variables
• categorical regression for unordered and ordered categories
  

Introduction to generalized linear mixed models

Introduction to generalized additive models

Readings/Bibliography

Recommended readings (a detailed list of selected chapters and sections is available on virtuale.unibo.it):

• Fahrmeir, L., Kneib, T., Lang, S. and Marks, B. (2021) Regression. Models, Methods and Applications. Second edition. Springer.
• Everitt, B. S., Hothorn, T. (2009) A handbook of statistical analysis using R. Second edition. Chapman & Hall/CRC.
  

Handouts provided by the teacher.

Other readings:

• Azzalini, A. (1996) Statistical inference based on the likelihood. Chapman & Hall/CRC.
• Agresti, A. (2015) Foundations of linear and generalized linear models. Wiley.
• Dobson, A. J. (2002) An Introduction to Generalized Linear Models. Second Edition. Chapman & Hall/CRC.

Teaching methods

Class lectures

Tutorial sessions in computer lab or using personal laptops in classroom

As concerns the teaching methods of this course unit, all students must attend Module 1 and 2 on Health and Safety online

Assessment methods

The exam will test the qualifications of each student on both a theoretical and a practical level.

The exam is based on a (possibly computer-based) quiz consisting of a set of multiple-choice and open-answer questions concerning the models presented during the course. These questions focus both on theoretical properties and on output produced using the software R. As far as the multiple-choice questions, correct answers are marked with 1 point, wrong answers are marked -0.20 points and missing answers 0 points. Each open-answer question receives a mark ranging between 0 and 2, depending on the correctness of the answer and the appropriateness of the terminology. The maximum time allowed to complete the quiz is 80 minutes. The total number of multiple-choice and open-answer questions may vary from sitting to sitting, and the final marks are always rescaled on a 0-31 range. Non-integer final marks are rounded down to the next small integer. Final marks larger that 30 are rounded down to 30. Final marks equal to 31 are considered 30 cum laude.

Students are allowed to reject a positive mark and retake the exam in one of the following sittings at least once but no more than twice.

Consulting textbooks or personal notes during the exam is not allowed.

As far as the first sitting is concerned, students have the option of splitting the exam into two partial exams (maximum time for each partial exam: 40 minutes). The first partial exam takes place after the first 5 weeks and is focused is focused on the topics covered during the first part of the course (the maximum mark for the first partial exam is set to 15.5). The second partial written exam is scheluled after the end of the course, and it covers the topics addressed during the second part of the course (the maximum mark for the second partial exam is set to 15.5). Students must take both partial written exams. In particular, in order to register for the second partial exam, a student must have taken the first partial exam. Furthermore, students taking the first partial exam are not allowed to take the total exam during the first sitting after the end of the course. In case of failure or rejection of the total mark obtained at the end of the second partial exam, students must repeat the whole written exam in one of the following sittings.

Office hours

See the website of Giuliano Galimberti

See the website of Saverio Ranciati