# Nonlinear (Mixed) Data Analysis

Vak
2023-2024

There are no entry requirements for the course. However, we assume that students are acquainted with the contents of the following courses of the Statistics & Data Science program:

• Linear algebra

• Linear and generalized linear models

• Statistical computing with R

## Description

Studying the relationship between two (or maybe three) variables is easy; you can visualise them in two-dimensional (or maybe three-dimensional) graphs. However, when you are interested in the relationship between than three variables, the human brain often falls short and you need specialised methods to get more insight in the dependencies between either cases or variables, even more so if the relations are not linear.

Many of these methods include the option to transform data. Transformations can help to reduce the dimensionality, accommodate nonlinear relationships, and take the properties of different types of variables into account in the case of mixed data.

In this course, we will discuss several methods that examine the (nonlinear) relationship between multiple variables simultaneously by reducing the dimensionality of the data.

The techniques that will be covered in class are:
a) Linear and optimal scaling regression analysis (i.a. catreg)
b) Linear and optimal scaling principal components analysis (i.a. catpca)
c) Multiple correspondence analysis
d) Classical scaling analysis (i.a. pcoa and isomap)
e) Multidimensional scaling analysis (i.a. Sammon mapping)
f) Nonlinear dimension reduction (i.a. t-SNE, UMAP)
g) Clustering (i.a. k-means and hierarchical)

## Course Objectives

By the end of the course, students can:
1. motivate which technique is suitable to answer a research question about a particular dataset;
2. discuss the differences in the assumptions and objectives of the techniques covered in the course;
3. identify the different parts of the loss functions of techniques covered in the course;
4. program some of the algorithms in R.
5. analyse data using the various techniques discussed in the course and evaluate the results.

## Timetable

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.
MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).
For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

## Mode of Instruction

The course consists of one course-day per week in which we focus on exercises to understand the workings of the various techniques. Students are expected to prepare for each exercise class by, for example, reading the literature, watching the lecture videos, and making preparatory exercises.

Make sure you have a laptop available during each lecture with SPSS version 27 or higher and the latest version of R and R-Studio (for details see Brightspace).

## Assessment method

• Two partial exams: each exam is 1/3 of final grade and should be at least 5.0 to pass the course

• Four home assignments: mean of assignments is 1/3 of final grade

Resit opportunities:

• Partial exams: there are resit exams for each partial exam.

• Home assignment: There are no resit opportunities for the individual home assignments, but there is one resit assignment that can replace the lowest grade of the four home assignments.

Reading material will be announced at the start of the course via Brightspace and is available via Leiden University Library.

## Registration

It is the responsibility of every student to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.

## Contact

Course coordinator: Dr. Sanne Willems (s.j.w.willems@fsw.leidenuniv.nl)