SUMM/Overview/Roadmap: multivariate

[josef-pkt]

What's the status and roadmap for multivariate Statistics

main methods

either available or started in statsmodels (or related packages)

• Models

  • _MultivariateOLS
  • SUR
  • ...
  • GMM (can we get more explicit or direct multivariate, multi equation support?)
  • panel data, GEE, system of equations, VAR, VECM, multivariate statespace models,
    two-part or multi-part models (e.g. heckman type, bivariate Probit)
    many related models, not in narrow definition of multivariate statistics
  • large sparse versions of Models

• Principal Components Analysis (PCA)

• Canonical Correlation Analysis (CCA)

• Factor Analysis

other methods

some are available in scikit-learn, those are not high priority unless there are specific results statistics that are important.

• Partial Least Square (PLS)
• Classical Multidimensional Scaling (MDS)
• Linear Discriminant Analysis (LDA)
• Multiclass LDA
• Independent Component Analysis (ICA), FastICA
• Probabilistic PCA
• Kernel PCA
• Correspondence Analysis
• Cluster Analysis (scipy)
• analogues for ordered variables: ?, e.g. item response models
• Redundancy Analysis

standalone and supporting hypothesis tests

hypothesis tests and related statistics including confidence intervals

• tests on mean, Hotelling, multivariate control charts
• MANOVA
• tests of covariances and correlation, covariance structure analysis
• gof tests for distributions
• rank test
• test for non-continuous data, e.g. multinomial, multivariate GLM
• non-Pearson correlation and association measures (polychoric, robust, regularized, ...),
  (kendalltau and spearman in scipy)

supporting code

• factor rotation, procrustes
• matrix tools
• multivariate transformation, e.g. compositional
• correlation_tools, closest positive definite
• missing values, imputation (what and where does it belong?)

R taskview also lists multivariate distributions including copulas

list of methods partially taken from https://github.com/JuliaStats/MultivariateStats.jl, TOC of Stata mv, and R taskview https://cran.r-project.org/web/views/Multivariate.html

Todo, Priorities

???
whatever someone is working on and contributes