Multivariate Analysis

Introducing to students to the analysis of the data in Veterinary Science by multivariate statistical techniques, first by revising techniques for bivariate data and following by using dependence and interdependence methods for multivariate data analysis. It is intended that the students acquire skills that enable them to identify situations in which it is possible and necessary a multivariate analysis of the data. As well as know used the R program results and interpret the outputs. Ultimate goals are: understand the techniques, how to apply them, the calculation of results through software tools and their interpretation.

The official memory of this degree includes the following contents.

Multivariate Analysis: dependence techniques, interdependence techniques. Comparing groups or treatments: ANOVA and MANOVA. Regression Models. Estimation. Prediction. Statistical inference. Identifying the group to which an object belongs: statistical techniques when the dependent variable is a categorical variable. The problem of separating groups: discriminant analysis. Dimensionality reduction: principal component analysis and correspondence analysis. Classification techniques: cluster analysis.

These contents will be developed in accordance with the following topics.

1. Multivariate Analysis in Veterinary Science.
A classification of multivariate techniques. R program: application in veterinary medicine

2. Basic concepts of statistical inference. A revision.
Initial data examination: missing data, outliers, normality, homoscedasticity. Estimation by confidence intervals. Estimation by hypothesis test.

3. Comparing groups or treatments. Analysis of variance.
Analysis of variance for single factor designs. Specific comparisons of means. Analysis of variance for two factor designs. Nonparametric techniques. Multivariate analysis of variance.

4. Regression Models.
Correlation. Simple linear regression. Inference on parameters and predictions. Curvilinear regression. Multiple regression. Collinearity. Methods of diagnosis.

5. Identifying the group to which an object belongs: statistical techniques when the dependent variable is a categorical variable.
Logistic regression. Testing for significance of the coefficients. Prediction. ROC curves.

6. The problem of separating groups: discriminant analysis.
Two group discriminant analysis. Assessing overall model fit and validation procedures. More than two groups.

7. Dimensionality reduction: principal component analysis and correspondence analysis.
Deriving components. Interpreting the components. How many components to retain? Introduction to factor analysis. Simple correspondence analysis.

8. Classification techniques: cluster analysis.
Hierarchical methods. Dendogram. Deriving clusters. Nonhierarchical cluster analysis: K-means. Principal components analysis with cluster analysis.

PRACTICAL LECTURES IN A COMPUTER LAB.
Data analysis using R and R- Commander:

-AM OR1: Revision of Biostatistics with R and R-Commander.
-AM OR2: Parametric and non-parametric test to compare sampled populations.
-AM OR3: Regression models: simple and multiple regression. Logistic regression. (1/2)
-AM OR4: Regression models: simple and multiple regression. Logistic regression. (2/2)
-AM OR5: Discriminant analysis.
-AM OR6: Dimensional analysis and associated graphs.
-AM OR7: Grouping data with cluster analysis.

SEMINAR SESSIONS
-AM S1: Review of basic concepts of statistical inference: Interpretation of results by computer.
-AM S2: Interactive approach to the statistical design of an experiment.

Estimated time for each thematic block (class hours). L= lectures hours, S = seminar sessions hours, I = interactive lectures hours.
Themes 1 & 2. Estimated time: 1L, 0S, 3I.
Theme 3. Estimated time: 2L, 1S, 3I.
Theme 4. Estimated time: 2L, 1S, 3I.
Themes 5 & 6. Estimated time: 2L, 1S, 3I.
Theme 7. Estimated time: 2L, 1S, 2I.
Theme 8. Estimated time: 1L, 0S, 1I.

Basic bibliography:
-Daniel, W. W. (2006): Bioestadística: base para el análisis de las ciencias de la salud. Limusa Wiley coop.
-Ekstrom,C. T.; Sorensen, H. (2014). Statistical Data Analysis for the Life Sciences. CRC Press.
-Everitt, B. S.; Hothorn, T. (2010): A Handbook of statistical Analyses Using R. Chapman & Hall/CRC.
-Grafen, A.; Hails, R. (2003). Modern Statistics for the Life Science. Oxford University Press.
-Kaps, M.; Lamberson, W. (2004): Bioestatistics for Animal Science. CABI Publishing.
-Martínez González, M. A. (ed) (2006): Bioestadística amigable. Díaz de Santos.
-Peña Sánchez de Rivera, D. (2002): Análisis de datos multivariantes. Mc Graw Hill.
-Rencher, A. C. (2002): Methods of multivariate analysis. Wiley
-Zar, J. H. (2010): Biostatistical Analysis. Pearson.

Complementary bibliography:
-Aldás, J.; Uriel, E. (2017): Análisis multivariante aplicado con R. Paraninfo.
-Álvarez Cáceres, R. (2007): Estadística aplicada a las Ciencias de la Salud. Díaz de Santos.
-Bate, S.T; Clark, R. A. (2014): The design and statistical analysis of animal experiments. Cambridge University Press.
-Denis, D.J. (2020). Univariate, Bivariate, and Multivariate Statistics Using R. Wiley
-Everitt, B. (2005). An Rand S-PLUS Companion to Multivariate Analysis. Springer
-Everitt, B. y Hothorn, T. (2011). An Introduction to Applied Multivariate Analysis with R. Springer
-Guisande González C. et all (2011): Tratamiento de datos con R, Statistica y SPSS. Díaz de Santos.
-Hair, J. F. et all (2004): Análisis multivariante. Prenticen Hall.
-Herrera Haro, J. G.; García Artiga, C. (2010): Bioestadística en Ciencias Veterinarias (Procedimientos de Análisis con SAS). Universidad Complutense de Madrid.
-Johnson, D. E. (2000): Métodos Multivariados aplicados al análisis de datos. Internacional Thomson Editores.
-Logan, M. (2010): Biostatistical design and analysis using R: a practical guide. Wiley-Blackwell.
-Maindonald, J.; Braun, W. J. (2010): Data Analysis and Graphics Using R. An Example-Based Approach. Cambridge.
-Martín Alvarez P.J. (2006): Prácticas de tratamiento estadístico de datos con el programa SPSS para windows: aplicaciones en el área de ciencia y tecnología de alimentos. Consejo Superior de Investigaciones Cientificas.
-Pardo, A.; San Martín, R. (2010): Análisis de datos en ciencias sociales y de la salud II. Editorial Síntesis.
-Pérez López, C. (2024): Análisis Multivariante de Datos. Aplicaciones con R. Ibergarceta Publicaciones.
-Petrie,A.; Watson,P. (2006): Statistics for Veterinary and Animal Science. Blackwell.
-Quinn, G. P., Keough, M. J. (2002): Experimental Design and Data Analysis for Biologists. Cambridge University Press.
-Rial Boubeta, A.; Varela Mallou, J. (2008): Estadística práctica para investigación en Ciencias de la Salud. Ed. Netbiblo.
-Véliz Capuñay, C. (2017): Análisis multivariante. Métodos estadísticos multivariantes para la investigación. Cengage Learning Editores.
-Zelterman, D. (2015). Applied Multivariate Statistics With R. Springer

General Competencies
GVUSC01. Ability to learn and adapt.
GVUSC02. Capability for analysis and synthesis.
GVUSC03. General knowledge of the working area.
GVUSC04. Work planning and management.
GVUSC05. Capability to put knowledge into practice.
GVUSC06. Capability to work both independently and as part of a team.
GVUSC07. Ability to work in an international context.
GVUSC08. Leadership, initiative and entrepreneurship.
GVUSC09. Ability to communicate in different areas.
GVUSC10. Ethical commitment and assumption of responsibilities.

Specific Competencies
Disciplinary specific Competencies
CEDVUSC 01. Generic knowledge of animals, their behaviour and the basis for their identification.
CEDVUSC 13. To know the organizational, economic and management aspects in all fields of the veterinary profession.

Specific Professional Competencies
D1VUSC 03. Perform standard laboratory tests, and interpret clinical, biological and chemical results.
D1VUSC 15. Technical and economic advice and management of veterinary companies in the context of sustainability.
D1VUSC 17. Perform technical reports specific to veterinary competencies.

Specific Academic Competencies
CEAVUSC 01. Analyze, synthesize, solve problems and take decisions in the professional areas of the veterinarian.
CEAVUSC 03. Divulge the information obtained during the professional practice of the veterinarian in a fluid, oral and written form, with other colleagues, authorities and society in general.
CEAVUSC 04. Search and manage information related to the activity of the veterinarian.
CEAVUSC 05. Know and apply the scientific method in professional practice including evidence-based medicine.
CEAVUSC 06. Knowing how to find professional help and advice.
CEAVUSC 07. Have basic knowledge of a foreign language, especially in technical aspects related to Veterinary Sciences.
CEAVUSC 08. Being aware of the need to keep professional skills and knowledge up-to-date through a process of lifelong learning.

Transversal Competencies
CTVUSC 01. Capacity for reasoning and argument.
CTVUSC 02. Ability to obtain appropriate, diverse and up-to-date information through a variety of media, including bibliographic information and the Internet, and to critically analyse it
CTVUSC 03. Ability to develop and present an organized and understandable text.
CTVUSC 04. Ability to hold a public exhibition in a clear, coherent and concise way.
CTVUSC 05. Skill in the use of ICTs.
CTVUSC 06. Use of information in a foreign language.
CTVUSC 07. Ability to solve problems through integrated application of their knowledge.

Teaching methodology will include lectures and interactive sessions, as well as supervised learning and assignments.

All the lectures will take place in computer room. Practical examples will be solved and discussed during every lecture. Different exercises, announced in bulletins will be delivered to students in order to encourage their personal work.

This subject will be among the ones offered by USC-Virtual (Virtual Campus of the USC). In the USC-Virtual web site all the material of supporting of the class sessions will be found (presentations, exercises, data for solving examples and practices...). The information related to the follow-up of the subject and to the autonomous work (calendar of work, groups of practices, scientific articles to revise...) will also appear in the web-site. The resolved doubts and the all the resources offered will be available from the virtual Campus of the USC.

The lectures and interactive sessions will be given in the Seminar of the Department of the subject in the Faculty of Sciences.

The evaluation of the subject will be done through continuous evaluation and evaluation activities at the end of the semester:
1.- The exam of the subject, at the end of the semester, will have a maximum valuation of 5 points in the final grade.
The evaluation at the end of the semester will be done by means of a written test with questions, mainly practical, on the concepts, models and procedures studied in the classes.
There will be two opportunities which will take place on the official dates set by the centre.

2.- The continuous assessment activities will be given a maximum of 5 points in the final grade.
Throughout the course, activities will be proposed for the evaluation of the continuous monitoring of the classes, assessing the participation and performance in the expository and interactive classes, as well as the elaboration of the works and problems that are proposed at the end of each subject. This work will be carried out outside the teaching timetable, and must be handed in within the deadlines established through the virtual campus.


The delivery dates of these works will be the following:
1st activity in week 3
2nd activity in week 5
3rd activity in week 7
4th activity in week 9
5th activity in week 11

The weighting of each of these activities will be 20% of the final mark of the continuous assessment.
The marks obtained in this section 2 of the first opportunity are retained for the second opportunity of the academic year.

There are no different assessment criteria for students who have been granted dispensation from attendance.

The final exam will be face-to-face.

In order to pass the subject it will be necessary to:
- Obtain at least 2 points (out of 5) in the final assessment test.
- Obtain at least 2 points (out of 5) in the continuous assessment activities.
- Obtain at least a grade of 5 in the continuous assessment and final assessment activities combined.
In the case of not obtaining at least 4 points (out of 10) in the evaluation test at the end of the semester, this will be the grade for the subject. Otherwise, the mark for the subject will be the sum of the mark for the final assessment test and the mark for the continuous assessment.

For those students who repeat the subject, and their mark in section 2 of the previous course is greater than or equal to 5 (out of 10), the mark from the previous course is kept in section 2. In this case, the note from section 2 of the current course will be the maximum between the mark of section 2 of the past year and the mark of section 2 of the current course.

For cases of fraudulent performance of exercises or tests, the provisions of the "Regulations on the assessment of students' academic performance and review of grades" shall apply.

ECTS: 3

Lectures (AM): 10 h.
Interactive lectures (AM OR, AM S): 19 h.
Tutorial support sesión (AM T): 1h
Total classroom work: 30h.

Autonomous work:
Individual study, revision of concepts:15h
Preparation of papers: 4h
Bibliographic review: 2h
Development of the proposed activities, exercises: 18h
Carrying out exams: 2h
Other proposed tasks: 4h

Autonomous work (estimation): 45 h.

Total estimated hours: 75 h.

- Regular attendance to lectures and practical sessions.
- The student must work on all the activities recommended by the professor (solving exercise, revising bibliography and practical exercises.
- Make use the tutorial sessions to solve doubts.
- Use the Virtual Campus (USC) as a communication channel between the students and the professor.

The student must have passed the first-year subject "Biostatistics".
The subject is taught in the two official languages of the Autonomous Community.