Advanced Statistical Models

Code:

M4147

Acronym:

M4147

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Computational Statistics and Data Analysis

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
E:BBC	0	PE_Bioinformatics and Computational Biology	1	-	6	42	162
M:BBC	2	The study plan since 2018	1	-	6	42	162
M:ECAD	9	Study plan since 2021/2022.	1	-	6	42	162

Teaching language

Suitable for English-speaking students

Objectives

1. Enable students with advanced regression methodologies, including repeated measures and longitudinal data analysis: general linear model and generalized linear models with mixed effects.
2. Implement statistical analysis in suitable software
3. Promote critical thinking throughout the statistical modeling process (data collection, modeling, interpretation of results, ...)

Learning outcomes and competences

1.Identification of scenarios of repeated measurements, longitudinal data or survival analysis
2. Identification of the most adequate model to the context of a given problem, among the studies models
3. Application and implementation of the studied models in R
4. Adequate interpretation of the results
5. Promotion of a critical thinking along the whole modelling process

Working method

Presencial

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

Previous knowledge on multiple linear regression and logistic regression (obtained, for instance, in Applied Statistics from the 1st semester)

Program

Multiple testing. Control of the Family-Wise Error Rate (FWER) and False Discovery Rate (FDR). 

General linear model. Modelling of the variance-covariance matrix of the random errors.

Mixed-effects linear model.

Experimental Design: randomized complete-block designs; factorial designs;  ANOVA models with random effects.

For each of the listed models, the following will be studied: models and their theoretical assumptions, parameters’ estimation and inference processes, modeling and implementation in the statistical programming language R, model selection and comparison, diagnostics, interpretation of results. Several examples of application will be presented.

Mandatory literature

José Pinheiro e Douglas Bates; Mixed Effects Models in S and S Plus , Springer, 2000. ISBN: ISBN-13: 978-1475781441
Verbeke G. & Molenberghs G. ; Linear Mixed Models for Longitudinal Data, Spinger, New York, 2000

Complementary Bibliography

Zuur Alain F., ed. lit. 340; Mixed effects models and extensions in ecology with R. ISBN: 978-1-4419-2764-4
Garrett M. Fitzmaurice; Applied longitudinal analysis. ISBN: 978-0-470-38027-7
Cabral M.S. & Gonçalves M.H. ; Análise de Dados Longitudinais, Sociedade Portuguesa de Estatística, 2011
Molenberghs, G. and Verbeke, G.; Models for Discrete Longitudinal Data, Spinger, New York, 2005

Teaching methods and learning activities

Classes are of theoretical-practical type. They include theoretical exposition, implementation of the studied models in the statistical programming language R, and interpretation and discussion of the results obtained. The examples presented and proposed exercises will start from real data, whenever possible.

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

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	90,00
Frequência das aulas	42,00
Trabalho escrito	30,00
Total:	162,00

Eligibility for exams

Sem requisitos.

Calculation formula of final grade

Students have to perform a written report, with an oral presentation, and a final exam.
The assignement is mandatory and its mark cannot be improved.

The final mark will be given by


where

A: mark of assignment
E: mark of the exam. 

For final approval, students have to score more than 5 values (out of 20) on each of the evaluation components.

Classification improvement

The mark obtained in the assignements cannot be improved.

Observations

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