ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 20 Interactive Classroom: 15 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
In this subject, the aim is to familiarize students with regression models, trying to obtain the following learning results:
- To know the generalized linear regression models.
- Know how to use advanced regression techniques (generalized regression and mixed models) autonomously for decision making in multidisciplinary contexts.
- Know how to formulate and apply the appropriate model to study the dependence between a variable and a set of explanatory variables.
- To know different extensions of the linear regression, identifying the differential factors of each one.
Chapter 1. Introduction to generalized linear models.
Introduction to generalized linear modelos. The Poisson model for count data. Parameter estimation and inference. Model contrast using deviance. Over-dispersion in the Poisson model. Formulation and analysis of generalized linear models
Chapter 2. Non-linear regression.
Remarkable examples of non-linear regression models. Estimation of parameters by least squares. Estimation algorithms. Inference on the parameters based on the asymptotic distribution and by means of the RSS profile. The F test.
Chapter 3. Quantile regression.
Introduction: the median, the quanta, the absolute deviation and the quantile loss function. The quantile regression function. The linear quantile regression model. Estimation algorithms. Properties of the quantile estimator. Inference on parameters. Non-linear quantile regression. Non-parametric quantile regression.
Chapter 4. Analysis of variance with random effects.
A review on ANOVA and ANCOVA models. Introduction to multilevel data. Analysis of variance model with random effects. Model estimation. Prediction of random effects.
Chapter 5. Multilevel models with continuous response.
Models with explanatory variable associated with the lower level: random effects on the trend and on the ordinate at the origin. Models with explanatory variable associated with the group. Intra-group, inter-group and contextual effect correlations. Estimation by restricted maximum likelihood. Validation and diagnosis. Prediction of random effects.
Chapter 6. Multilevel models with binary response.
Formulation of the logistic regression model with random effects. Estimation methods. Interpretation of the elements of the model in the logistic case.
Basic Bibliography:
[1] Faraway, J.J. (2006). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman and Hall.
[2] Koenker, R. (2005). Quantile regression. Cambridge University Press.
[3] McCulloch, C.E. and Neuhaus, J.M. (2005). Generalized linear mixed models. Encyclopedia of Biostatistics, 4.
[4] Ritz, C. and Streibig, J.C. (2008). Nonlinear regression with R. Springer. Available at: https://link.springer.com/book/10.1007/978-0-387-09616-2.
[5] Sheather, S.J. (2009). A modern approach to regression with R. Springer.
[6] West, B. T., Welch, K. B. and Galecki, A. T. (2014). Linear mixed models: a practical guide using statistical software. Chapman and Hall/CRC.
Complementary Bibliography:
[1] Furno, M. and Vistocco, D. (2018). Quantile regression: estimation and simulation (Vol. 216). John Wiley & Sons. Available at: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118863718.
[2] Galecki, A. and Burzykowski, T. (2013). Linear mixed-effects models using R: A step-bystep approach. Springer Science & Business Media. Available at: https://link.springer.com/book/10.1007/978-1-4614-3900-4.
[3] Huet, S., Bouvier, A., Gruet, M.A. and Jolivet, E. (1996). Statistical tools for nonlinear regression (A practical guide with S-Plus examples). Springer. Available at: https://link.springer.com/book/10.1007/b97288.
In this subject, the basic, general and transversal competences included in the report of the master will be worked on. The specific competences that will be promoted in this subject are indicated below:
E1 - To know, identify, model, study and solve complex problems of statistics and operational research, in a scientific, technological or professional context, arising in real applications.
E2 - Develop autonomy for the practical resolution of complex problems arising in real applications and for the interpretation of results to aid in decision making.
E3 - To acquire advanced knowledge of the theoretical foundations underlying the different methodologies of statistics and operational research, allowing for their specialized professional development.
E4 - Acquire the necessary skills in the theoretical-practical management of probability theory and random variables that allow for their professional development in the scientific/academic, technological or specialized and multidisciplinary field.
E5 - To deepen the knowledge in the specialized theoretical-practical foundations of the modeling and study of different types of dependency relationships between statistical variables.
E6 - Acquire advanced theoretical-practical knowledge of different mathematical techniques, specifically oriented to help in decision making, and develop reflection capacity to evaluate and decide between different perspectives in complex contexts.
E8 - Acquire advanced theoretical-practical knowledge of techniques aimed at making inferences and contrasts related to variables and parameters of a statistical model, and know how to apply them with sufficient autonomy in a scientific, technological or professional context.
The teaching will consist of lectures and interactive classes, as well as the learning mentoring and the tasks entrusted to the students. Notes on the subject will be provided, as well as other material to guide the learning of the software.
In the lectures and interactive classes, examples will be solved by means of the R software, so it is necessary for the students to have a computer. Activities for students will be proposed, which will consist of solving questions, exercises and examples related to generalized regression models and mixed models.
The following is an approximation of the hours that will be dedicated to each topic:
THEME 1.INTRODUCTION TO GLM (4h lectures, 3h labs)
TOPIC 2. NON-LINEAR (2h lectures, 2h labs)
TOPIC 3. QUANTILITY (2h lectures, 3h labs)
TOPIC 4. RANDOM ANOVA (2h lectures, 4h labs)
TOPIC 5. CONTINUOUS MULTILEVEL (3h lectures, 5h labs)
TOPIC 6. BINARY MULTILEVEL (2h lectures, 3h labs)
In the case that some of the teaching activities must be carried out online, the MS Teams platform will be used, which is institutional for the USC and the UDC, with guest access for students registered at UVigo.
Continuous assessment (40% of final mark): continuous assessment will be carried out based on the resolution of problems by the students. In these problems, students will use the R program and write down and/or present the conclusions drawn. The qualification obtained will be kept between the opportunities (ordinary and extraordinary) within the call of each course. With the different activities that will be proposed throughout the course, the level of acquisition of the basic and general competences will be valued, CB6- CB10 and CG1-CG5. The level reached in the transversal competences CT1-CT5 and the specific competences E2 and E6 will also be assessed.
Final exam (60% of final mark): the final exam will consist of several theoretical and practical questions on the contents of the subject, within which the interpretation of the results obtained with the statistical language used in interactive teaching (R) may be included. The test will evaluate the acquisition of the specific competences E1, E3, E4, E5 and E8.
Assessment presentation: a student is considered to attend an assessment when he/she participates in activities that allow him/her to obtain at least 50% of the final assessment. The weight of the continuous assessment in the extraordinary opportunity (July exams) will be the same as in the ordinary assessment. At the second assessment opportunity, a exam will be taken and the final score will be the maximum of three amounts: the score of the ordinary evaluation, the score of the new exam and the weighted average of the new exam and the continuous assessment.
Each ECTS credit translates into 7 hours of classroom instruction. It is estimated that students will need one hour to prepare the material corresponding to each classroom hour, prior to the session itself. Afterwards, they will need an hour and a half to understand the contents, including the activities associated with exercises and other tasks. A total of 24.5 hours per ECTS credit will result.
It is desirable that students have basic knowledge of probability and statistics. It is also advisable to have average skills in the use of computers, and specifically statistical software. For a better learning of the subject, it is convenient to keep in mind the practical sense of the methods that are being learned.
To successfully pass the subject, attendance at classes is advisable, with daily monitoring of the work done in the classroom being essential. The teacher will inform the class of the weekly plan, indicating the learning objectives to be achieved and the contents to be worked on during the corresponding week.
LEARNING RESOURCES
Students will have notes prepared by the subject's teachers, as well as the bibliography recommended in this program. For the dissemination of the subject's own material, the master's website will be used.
The development of the contents of the subject will be carried out taking into account that the competences to be acquired by the students must comply with the level MECES3. The contents included in this subject are technically complex (such as those considered in generalized linear models) and/or highly specialized and innovative (for example, those related to multilevel models), and their study will be accompanied by practical implementations, using specific software.
In the case of fraudulent exercises or tests, the provisions of the respective regulations of the universities participating in the Master in Statistical Techniques will apply.
This guide and the criteria and methodologies described in it are subject to the modifications derived from the regulations and guidelines of the universities participating in the Master in Statistical Techniques.
Rosa María Crujeiras Casais
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813212
- rosa.crujeiras [at] usc.es
- Category
- Professor: University Professor
Mercedes Conde Amboage
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mercedes.amboage [at] usc.es
- Category
- Professor: Temporary PhD professor
| 01.24.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |
| 06.30.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |