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Dichotomous Key for Multivariate Statistics

Follow each step in order. Each step either leads to a method or to the next step.

1. Is there a defined dependent (outcome) variable?

  • Yes → go to Step 2
  • No / exploratory analysis → go to Step 6

2. Type of dependent variable

  • Categorical → go to Step 3
  • Continuous → go to Step 4
  • Multiple continuous dependent variables → go to Step 5

3. Categorical dependent variable

  • Two categories → go to Step 3a
  • More than two categories → go to Step 3b

3a. Two categories

  • Predictors continuous, assumptions met (normality, equal covariance) → LDA (Linear Discriminant Analysis)
  • Predictors continuous and/or categorical, or assumptions violated → Logistic Regression

3b. More than two categories

  • Ordered categories → Ordinal Logistic Regression
  • Unordered categories → Multinomial Logistic Regression

4. Continuous dependent variable

  • Predictors continuous and/or categorical → Multiple Linear Regression
  • Predictors categorical only (± continuous covariates) → ANOVA / ANCOVA

5. Multiple continuous dependent variables

  • Predictors present → MANOVA / MANCOVA
  • No predictors → go to Step 6

6. Exploratory analysis (no dependent variable)

  • Goal: reduce dimensionality or find structure → go to Step 7
  • Goal: constrained ordination with explanatory variables → go to Step 9
  • Goal: group observations → go to Step 10
  • Goal: classify observations into known groups → go to Step 12
  • Goal: relate two sets of variables → go to Step 13
  • Goal: test group differences on a distance matrix → PERMANOVA

7. Dimension reduction (unconstrained)

  • Variables continuous, Euclidean distance appropriate → PCA
  • Distance or dissimilarity matrix required → go to Step 8
  • Species or community data with unimodal responses → CA (Correspondence Analysis)
  • Latent constructs or model-based factors → Factor Analysis

8. Distance-based ordination (unconstrained)

  • Non-metric, rank-based, iterative → NMDS
  • Metric, eigen decomposition, variance explained → PCoA

9. Constrained ordination (with explanatory variables)

  • Response variables continuous, linear responses → RDA (constrained PCA)
  • Response variables with unimodal responses (species data) → CCA (constrained CA)
  • Any distance matrix with explanatory variables → db-RDA (constrained PCoA)

10. Clustering

  • Number of clusters known in advance → K-means Clustering
  • Number of clusters unknown → go to Step 11

11. Unknown cluster structure

  • Hierarchical structure desired → Hierarchical Clustering
  • Density-based, arbitrary shapes → DBSCAN
  • Soft assignment, overlapping groups → Fuzzy Clustering

12. Classification into known groups

  • Linear decision boundaries, assumptions met → LDA
  • Unequal covariances between groups → QDA (Quadratic Discriminant Analysis)
  • Many predictors (p approaches or exceeds n) → LASSO Logistic Regression

13. Relating two sets of variables

  • Both sets continuous → CCorA (Canonical Correlation Analysis)
  • One set categorical, one set continuous → go to Step 12
  • Distance-based relationships with explanatory variables → db-RDA
  • Many predictors or collinearity → PLS (Partial Least Squares Regression)

Abbreviations

Unconstrained ordination

  • PCA = Principal Component Analysis — linear, Euclidean distances
  • CA = Correspondence Analysis — unimodal species responses, chi-square distances
  • PCoA = Principal Coordinates Analysis — eigen decomposition of any distance matrix
  • NMDS = Non-metric Multidimensional Scaling — non-metric, iterative, rank-preserving

Constrained ordination

  • RDA = Redundancy Analysis — constrained PCA (linear responses)
  • CCA = Canonical Correspondence Analysis — constrained CA (unimodal responses)
  • db-RDA = Distance-based Redundancy Analysis — constrained PCoA (any distance matrix)

Regression and modelling

  • MLR = Multiple Linear Regression
  • ANOVA = Analysis of Variance
  • ANCOVA = Analysis of Covariance
  • MANOVA = Multivariate Analysis of Variance
  • MANCOVA = Multivariate Analysis of Covariance
  • PLS = Partial Least Squares Regression

Classification

  • LDA = Linear Discriminant Analysis
  • QDA = Quadratic Discriminant Analysis

Other

  • CCorA = Canonical Correlation Analysis — relates two sets of continuous variables (distinct from CCA above)
  • PERMANOVA = Permutational Multivariate Analysis of Variance
  • DBSCAN = Density-Based Spatial Clustering of Applications with Noise