Generalized Linear Models

Code:

M4141

Acronym:

M4141

Keywords
Classification	Keyword
CNAEF	Mathematics and statistics

Instance: 2021/2022 - 1S (edição n.º 1)

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Computational Statistical Modelling

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
E:MEC	12	PE_Computational Statistical Modelling	1	-	3	21	81

Teaching language

Portuguese and english

Objectives

1. To correctly identify regression scenarios and the corresponding model
2. To perform independent statistical analysis and to implement them in R
3. To correctly interpret the obtained results, either by using additive or interaction effects
4. To understand the importance of the evaluation of the model's goodness-of-fit, and to knao how to conduct it
5. Critical analysis of the results

Learning outcomes and competences

At the end of the curricular unit, students are expected to:
1. recognize regression scenarios and know how to select an appropriate model
2. know how to correctly conduct a data analysis involving regression models, using R
3. correctly interpret the obtained results, either with additive effects or with interaction effects in the explanatory variables
4. critically analize the models' goodness-of-fit
5. develop a critical spirit in the interpretation of results.

This curricular unit follows the unit Estatística Aplicada (Applied Statistics) generalizing the linear regression modl to more general response variables. It therefore aims to complement the students background in regression modelling.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of the standard linear regression model.

Program

1. Exponential family of distributions. General structure of the generalized linear models.
2. Logistic regression
3. Poisson regression. Negative Binomial regression.

In 2. and 3., the following topics will be approached: link function, specific structure of the model, estimation methods, categorical predictors, interpretation of regression coefficients, interactions, goodness-of-fit, model assumptions, residuals analysis, model fitting in R.

Mandatory literature

Rita Gaio; Apontamentos escritos pela professora

Complementary Bibliography

Faraway, J.; Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Chapman & Hall/CRC Texts in Statistical Science. ISBN: 158488424X
Ludwig Fahrmeir; Multivariate statistical modelling based on generalized linear models. ISBN: 0-387-95187-3
Lindsey, J.K. ; Applying generalized linear models, Springer. ISBN: 0-387-98218-3

Teaching methods and learning activities

Classes are theoretical-practical. They include interactive 
theoretical exposition, encouraging student participation, 
and a practical component of implementing the models studied 
in statistical analysis software, with consequent interpretation 
and discussion of the results obtained. Books and scientific 
articles will be used as a way to guide students to understand 
the issues. The examples presented and proposed exercises will be 
based on real data, whenever possible. The software used will be 
the programming language in the R software environment, 
with a free license.



Teaching methodologies will be adjusted to allow students 
to integrate the objectives of the course.

Software

R

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	40,00
Trabalho escrito	60,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	53,00
Frequência das aulas	21,00
Trabalho escrito	7,00
Total:	81,00

Eligibility for exams

To obtain at least 30% in the assignment.

Calculation formula of final grade

Final mark = 0.4*exam + 0.6*assignment.
The student will only be approved if he/she marks at least 30% on each evaluation component and the final mark is greater than or equal to 9.5 points (out of 20)

Classification improvement

The assignment cannot be improved.

Observations

1) The way the course will be provided is conditioned to the limitations imposed by FCUP according to the evolution of the COVID19 pandemic.

2) The evaluation method is conditioned by the evolution of the COVID19 pandemic.