Class 9 (Module II)

11 Abril 2022, 09:30 • Jorge Filipe Campinos Landerset Cadima

Linear Models [slides 298-321, 324-325, 327-332, 339-360] Again the two-way ANOVA model without interaction effects: interpreting the parameters with constraints alpha_1=beta_1=0; the lack of flexibility of the model, due to lack of parameters; some formulas. The two-way ANOVA with interaction effects: the model equation and its constraints; the need for three tests, one for each kind of effects; building the three F statistics, through the decomposition of the Total Sum of Squares; the rules to define degrees of freedom for model effects and for residual variability; the summary-table. Fitting two-way ANOVAs with interaction effects in R: two examples (with and without significant  interaction effects).Some formulas and some warnings. The Analysis of Covariance: introducing the concept through the problem of comparing simple linear regressions in k contexts, defined by a k-level factor. The full ANCOVA model, allowing for different regressions lines in each context. Simpler models (a single line for all contexts, parallel lines etc.) as submodels of the ANCOVA model, and the possibility of using partial F tests or Student's t-tests to study them. The relations between the full ANCOVA model and the simple linear regressions using the subset of data in each context. Interpreting the R^2 in an ANCOVA. Fitting ANCOVAs in R: examples and warnings. Generalised Linear Models [slides 1-13] Program and Bibliography. Introducing the concept throught the two extensions to Linear Models. Examples of distributions in the exponential family of distributions. The three components of a GLM in the classic formulation by McCullaugh & Nelder.
Nota: Esta aula foi leccionada na quarta-feira, dia 27.4.22, das 15h às 17h35, na Sala S3, simultaneamente presencial e por zoom.