What is this course about

• Often in experimental studies many outcomes are collected simultaneously.
• Sometimes the outcomes or response variables are of mixed types.
• Methods for the separate analysis of such outcomes are well established in the literature.
  • Continuous and symmetric data: linear regression models.
  • Continuous and assymetric data: gamma and inverse Gaussian regression models.
  • Semi-continuous data: Tweedie and zero-inflated regression models.
  • Counting data: Poisson, negative binomial, Poisson-Tweedie and \(\ldots\) regression models.
  • Bounded data: logistic, probit, beta, simplex and \(\ldots\) regression models.

Main goal

• Purpose of this course is to present the state of art in

  Multivariate analysis of experimental data based on the multivariate covariance generalized linear models class.

Learnings objectives

• After this course participants will be able to
  • identify settings in which a multivariate analysis is required,
  • construct and fit an appropriate multivariate model, and
  • correctly interpret the obtained results.
• The course will be explanatory rather than mathematically rigorous
  • emphasis is given on sufficient detail in order for participants to obtain a clear view on the multivariate models and how they should be used in practice.

Outline

Part I: Multivariate analysis of Gaussian data (MANOVA)

• Motivational datasets and research questions.
• The General Multivariate (Gaussian) Linear Model.
  • Estimation and inference (least squares and MLE).
  • General linear hypotheses.
  • Multivariate hypotheses tests.
  • Computational implementation in \(\textsf{R}\).
  • Usage of the \(\texttt{lm()}\) and \(\texttt{manova()}\) functions.
  • Worked examples.
  • Assumptions and limitations.
  • Concluding remarks.

Part II: Multivariate analysis of non-Gaussian data (McGLM)

• Dealing with non-Gaussian data: Multivariate generalized linear models (MGLMs).
• Dealing with non-independent data: Linear covariance models (LCMs).
• Specifying the matrix linear predictor:
  • Mixed models.
  • Longitudinal studies.
  • Times series.
  • Genetic data.
• Dealing with non-independent and non-Gaussian data (McGLMs).
• Estimation and Inference.
• General linear hypotheses tests.
• MANOVA-like test for non-Gaussian data.
• MANOVA in the McGLM framework.
• The \(\texttt{mcglm()}\) function.
• Worked examples.
• Discussions and extensions.