Multivariate Analysis Study notes

Multivariate Data Analysis: Eurovision Example

• Eurovision Song Contest as a case study for multivariate data analysis.
• Objective: Determine if Eurovision judging is fair or if underlying patterns exist related to geopolitical relationships.
• Data: Matrix of countries scoring other countries' acts.
• Technique: Cluster analysis used to generate a dendrogram, revealing non-random patterns.
• Findings:
  • Nordic/Scandinavian block.
  • Greece and Cyprus cluster together.
  • UK and Ireland cluster together.
  • Bosnia and Turkey cluster.
• Conclusion: Voting is biased towards friendly nations rather than based purely on the quality of the acts.
• Representation: Multivariate data analysis can be represented in 2D or 3D mapping, showing clusters (e.g., Eastern, Nordic/Baltic, Western European blocks).
• Australia's chances: Australia is unlikely to win due to these geopolitical biases.

Course Overview: Techniques and Data

• First lecture: Focuses on the definition, collection, analysis, and exploration of multivariate data.
• Second lecture: Covers Principal Components Analysis and Factor Analysis.
• Other techniques:
  • Cluster Analysis.
  • Non-metric multi-dimensional scaling.
  • MANOVA (multivariate, analysis of variance) - similar to ANOVA but with multiple variables.

References

• Quinn and Keogh (old or new edition).
  • Chapters accessible online through the library.
  • Examples using soil samples and biodiversity.
  • Data available for download.
• Data chapter for free.

Course goals

• Understand major concepts such as ordination, principal components, factor analysis, non-metric multidimensional scaling, cluster analysis, MANOVA, and PerMANOVA.
  *Learn to make decisions about data and its interpretation.
  *To understand and interpret scientific papers using these techniques.

Multivariate Techniques: Key Themes

• Linear combinations of variables: A recurring concept.
• Distance/dissimilarity/similarity measures: Used repeatedly.
• Transformation of data: Note that its use differs from univariate transformation.
• Standardization.

Types of Multivariate Techniques

• Focus on ordination and clustering.
• Brief coverage of regression (multiple regression).
• Classification (some overlap with clustering).

Multivariate Data: Definition

• Multiple response variables.
• Variables are not necessarily independent; they interrelate.
• Examples:
  • Biodiversity of a park.
  • Physical properties of an environment (soil/water chemistry).
• Specialized approaches are needed because data often do not conform to traditional statistical assumptions.

Why use Multivariate Analysis

• Avoid conducting multiple ANOVAs on interrelated variables.
  • Problem: Type I errors (false positives) increase with multiple tests.
• Multivariate statistics consider the interactions of variables together.

Types of Questions Addressed

• Change in community composition.
• Differences in water quality.
• Changes in habitat characteristics.
• Organismal traits (phenotypic traits, diet effects).

Examples of Outputs

• Ordinations from principal components.
• Clustering diagrams.
• Non-metric multidimensional scaling plots.

Habitat Complexity: An Example

• Habitat complexity is a multivariate term, comprising multiple interrelated variables.
• Measurement:
  • Canopy cover.
  • Shrub cover.
  • Number of stems.
  • Diversity of trees/shrubs.
  • Number of logs.
  • Percentage of dirt cover.
  • Soil nutrients.
• Multivariate analysis can compare sites based on these variables.

Data Analysis

• Multivariate analysis summarizes existing data by measuring many variables.
• Simplifies data into fewer derived variables (e.g., principal components).
• Reduces Type I errors and reveals patterns.
• Applicable to soil characteristics, habitat, organismal traits, water quality, etc.

Good Practices

• Just because you can measure it, does not mean you should.

Brazil Football Example

• Skills measured:
  • Passing accuracy.
  • Kicking strength (ball speed).
  • Speed on angle tracks.
  • Overall strength.
• Principal components analysis results:
  • Skill Level: accuracy, technique, ball controle, etc..,
  • Athleticism Level: Physical strength and speed.