Sumários

Module III, Class 2

4 Maio 2021, 14:30 • Jorge Filipe Campinos Landerset Cadima

Online class, Monday May 17, 14h30-17h00
[Slides 45-85] Eigenvalues/vectors in R. More properties of PCs. PCA on standardized data (correlation matrix PCA): its purpose and properties. The correlation matrix PCA of the crayfish data. The effects of centering and scaling in the representation of the data in both spaces (R^p and R^n). Interpreting PCs: tools and warnings. An alternative property optimized by correlation matrix PCs. The generalized eigenvalue problem. The Singular Value Decomposition of a generic matrix. PCA as an SVD of the centred data matrix (divided by the square root of n-1). SVDs in R. Yet another view of PCA: approximating an nxp data matrix by an nxp matrix of lower rank; the Eckart-Young theorem.

Module III, Class 1

3 Maio 2021, 14:30 • Jorge Filipe Campinos Landerset Cadima

Online class, Tuesday May 11, 14h30-17h00

Multivariate Statistics [slides 1-44] Programme and bibliography. Introductory remarks regarding Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). A motivating example: the crayfish dataset. Some matrix concepts: orthogonal matrices; The classification of symmetric matrices through their quadratic forms; eigenvalues and eigenvectors and the spectral decomposition of symmetric matrices; properties and powers of diagonal matrices; powers of symetric matrices;the trace of a square matrix and the circularity of the trace; (co-)variance matrices as positive semi-definite matrices; variances and covariances of linear combinations of variables. PCA: a statistical introduction. The Rayleigh-Ritz Theorem. The definition of PCs and some properties. PCA in R. Exploring the PCs of the crayfish data.

Class 16, Module II

27 Abril 2021, 14:30 • Elsa Maria Félix Gonçalves

Online class Monday, May 10, from 14h30 and 17h00

Linear Mixed Models. Some particular cases. Exercises 3 and 4.

Class 15, Module II

26 Abril 2021, 14:30 • Elsa Maria Félix Gonçalves

Online class Friday, May 7, from 10h00 and 12h30

Linear Mixed Models. Some particular cases. Exercises 1 (cont.) and 3a).

Class 14, Module II

20 Abril 2021, 14:30 • Elsa Maria Félix Gonçalves

Online class Monday, May 3, from 14h30 and 17h00

Linear Mixed Models. Estimation of fixed effects and prediction of random effects; hypotheses tests for covariance parameters, fixed and random effects; model selection; validation of model assumptions.
Exercise 1: a), bi) and bii).