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 assess each student's knowledge and skills at both the theoretical and practical levels.

The use of AI or smart devices (including, but not limited to, smartphones, smartwatches, smart glasses, and earbuds) during the exam is strictly prohibited. Any such use constitutes a violation of academic integrity and will be reported to the appropriate University authorities for disciplinary review.

The exam consists of a written exam containing a set of multiple-choice and open-answer questions on the models presented during the course. These questions cover both theoretical aspects and output produced using the R software. Multiple-choice questions are graded as follows: each correct answer is awarded 1 point, each incorrect answer is penalized by 0.20 points, and unanswered questions receive 0 points. Each open-answer question is worth either 1.5 or 2 points, depending on its difficulty. The mark awarded ranges from 0 to the maximum available for that question, depending on the correctness of the answer and the appropriateness of the terminology used. The total number of multiple-choice and open-answer questions may vary from one exam sitting to another, while the maximum score remains fixed at 31 points. Non-integer final marks are rounded down to the next lower integer. A final mark of 31 is recorded as 30 cum laude.

Students will have 80 minutes to complete the written exam. Consulting textbooks or personal notes during the exam is not permitted.

Students may reject a passing grade and retake the exam at one of the subsequent exam sittings at least once but no more than twice.

For the first exam sitting after the end of the course, students may choose to split the exam into two partial written exams, each lasting 40 minutes. The first partial written exam takes place after the first five weeks of the course and covers the topics presented during the first part of the course (maximum score: 15.5 points). The second partial written exam is scheduled after the end of the course and covers the topics presented during the second part of the course (maximum score: 15.5 points). Students must take both partial written exams. In particular, to register for the second partial written exam, a student must have taken the first partial written exam (no minimum score is required). Furthermore, students who take the first partial written exam are not allowed to take the full written exam during the first exam sitting after the end of the course.

In the event of failure or rejection of the final mark obtained from the two partial written exams, students must repeat the entire written exam at one of the subsequent exam sittings.

Office hours

See the website of Giuliano Galimberti

See the website of