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# Multivariate analysis and multidimensional data analysis

Vak
2014-2015

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## Description

This course is about a large variety of methods for multivariate analysis and multidimensional data analysis. The first part (six course-days) deals with the analysis of measurements for N objects (persons) on P variables (attributes), and we typically wish to understand the relationships between those objects and variables. The data are usually given in one or more multivariate data matrices. The course extends classical approaches to multivariate analysis in various ways. We will not only deal with numeric, but also with categorical (both nominal and ordinal) multivariate data. In addition, we will be able to deal with nonlinear relationships between variables. Both extensions are part of the same optimal quantification/nonlinear transformation framework. Key concepts are dimension reduction and visualization (in principal components and correspondence analysis), and prediction and regularization (in multiple regression analysis).
The second part of the course (two course-days) is about a very important group of multidimensional techniques for the analysis of proximity data between objects (given in one or more N by N matrices) and preference data between row objects and column objects (in one or more N by M matrices). For the analysis of proximities and preferences, we use the terms multidimensional scaling and multidimensional unfolding, respectively. Here dimension reduction and visualization are of utmost importance by definition, while nonlinear transformations also play an important part.
The third part of the course (six course-days) will focus on classification methods. Here the interest is primarily in the question whether we can predict the class an object (subject, person) belongs to from a predefined set of classes given a set of explanatory variables. Two methods will be presented in detail: discriminant analysis and multinomial logistic regression. For both, dimension reduction will be discussed. Dimension reduction can be performed in a distance framework or in an inner product framework. These methods will be presented, and students will also learn how to program them in R.
Next to R, the first two parts of the course will also use the IBM-SPSS package CATEGORIES, which has been developed in Leiden.

## Time Table

For the course days, course location and class hours check the Time Table 2014-15 under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience

## Mode of Instruction

The course consists of 2 course-days per week. Each course-day contains a two-hour lecture and a two-hour practical.

## Assessment method

Assessment will be based on a written exam (50%) and 5 assignments (50%).

Date information about the exam and resit can be found in the Time Table 2014-15 pdf document under the tab “Masters Programme” at http://www.math.leidenuniv.nl/statscience. The exams take place in the Snellius building, the room will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed online at:“http://info.liacs.nl/math/”:http://info.liacs.nl/math/
If the exam does not take place in the Snellius building, then an announcement will be sent via blackboard

The written exam is a closed exam. Books, laptop, internet or any other sources of external information are not allowed during the exam.

Reading material will be announced at the start of the course.

## Registration

Enroll in Blackboard for the course materials and course updates.

To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

## Contact information

jmeulman [at] math [dot] leidenuniv [dot] nl

## Remarks

• This is a compulsory course in the Master’s programme of the specialisation Statistical Science for the Life & Behavioural sciences.