Linear Models

Overview

Linear regression. Non-singular case: analysis of variance, extra sum of squares principle, generalised least squares, residuals. Singular case: generalised inverse solution, estimable functions. Experimental designs: completely randomised, randomised block, factorial; contrasts, analysis of covariance; Generalised linear model (GLM): maximum likelihood and least squares; exponential family; Poisson and logistic models; model selection for GLM.

Learning Objectives

On completion of the module, it is intended that students will be able to: understand and use linear models and multiple linear regression for modelling a measured response as a function of explanatory variables using the least squares approach, and so perform model selection and diagnostics expanding their knowledge to the weighted least squares model; understand ANOVA as a method of analysis for experimentally designed data using non-singular and singular cases; apply the extra sum of squares principle to analyse and interpret residuals, the generalized inverse solution, and assess whether a function is estimable and the hypotheses testable; recognise, apply and interpret the results of analysis of variance for the completely randomized, randomized block, and factorial designs; demonstrate familiarity with using contrasts and apply analysis of covariance; upon developing a full understanding of linear models, extend this to Generalized Linear Models and apply them and model selection to discrete recorded responses using maximum likelihood and least square estimation for distributions from the exponential family, Poisson and logistic; build on their ability to use SAS for the development and selection of linear models.

Skills

Use of appropriate statistical software in applying linear and generalised linear models.

Assessment

None.