Multivariate Analysis
Multivariate analysis: from perception maps to segmentation
Four applied exercises using correspondence analysis, k-means, hierarchical clustering and exploratory and confirmatory factor analysis on survey and product data.
- Programme
- Multivariate Analysis · Master’s in Business Intelligence and Data Science, UEES
- Format
- Academic group project · team of two
- Period
- 2024
- Simple correspondence analysis
- Multiple correspondence analysis
- K-means
- Hierarchical clustering
- Exploratory factor analysis
- Confirmatory factor analysis
Overview
Multivariate analysis answers questions that involve many variables at once: how customers perceive competing brands, which products naturally group together, or which underlying factors explain dozens of survey answers.
This final course project applies six techniques to four different datasets, interpreting each result and translating it into conclusions that a business or an institution could act on.
The business problem
Simple descriptive statistics cannot show how several attributes interact. Segmenting products, mapping brand perception or validating a questionnaire requires techniques that reduce complexity without losing the structure of the data.
Methodology
- 01
Simple correspondence analysis
How 352 comic readers associate six statements with three publishers. The first dimension explained 74.4% of the differences and the second 25.6%, producing a clear perception map for each brand.
- 02
Multiple correspondence analysis
Relationships between sources of stress, marital status and education level in a psychology dataset. Sources of stress were the most discriminating variables in both dimensions.
- 03
K-means and hierarchical clustering
15 car models described by engine size, power, top speed, comfort, interior space and noise level. Variables were first reduced to two components — comfort and performance — and then grouped into three clusters.
- 04
Exploratory and confirmatory factor analysis
A 19-question Likert questionnaire on interest and motivation towards studying, answered by 299 students. The exploratory analysis identified four components; the confirmatory analysis then tested whether that structure held.
Documented results
- KMO sampling adequacy
- 0.820
- components identified
- 4
- of total variance explained
- 52.864%
- students · 19-item questionnaire
- 299
- car models grouped into clusters
- 15 → 3
- Component 1 24.060 %
- Component 2 13.501 %
- Component 3 9.520 %
- Component 4 5.783 %
View as table
| Component | % of variance |
|---|---|
| Component 1 | 24.060 |
| Component 2 | 13.501 |
| Component 3 | 9.520 |
| Component 4 | 5.783 |
| Cumulative | 52.864 |
Source: original project report (exploratory factor analysis, 299 students, 19 items).
-
Cluster 1 · 4 models
Higher comfort, lower performance
-
Cluster 2 · 8 models
Lowest comfort and performance
-
Cluster 3 · 3 models
Highest performance, lower comfort
Source: original project report. Variables were first reduced to two components: comfort and performance. Each mark represents one model.
Key findings
- The car models split into three segments: higher comfort with lower performance (4 models), lowest comfort and performance (8) and highest performance with lower comfort (3).
- The questionnaire data was suitable for factor analysis (KMO 0.820, significant Bartlett test), and four components explained 52.864% of the variance.
- The confirmatory analysis did not support the proposed model, even after modifications (CFI 0.86 and TLI 0.838, below the 0.90 benchmark). The conclusion: the instrument needs to be revised.
What this project demonstrates
- 1
Choosing a technique according to the data: correspondence analysis for categories, clustering and factor analysis for metric variables.
- 2
Linking statistical output to decisions — segments a car maker could target, or brand positions a publisher could reinforce.
- 3
Reporting a negative result honestly: a model that does not fit is a valid and useful finding.