Quantitative Methods What lies beyond What lies beyond

Quantitative Methods What lies beyond?

What lies beyond? General Linear Model What does GLM do for us? • • partitioning of variance and DF tests for whether x-variables matter statistical elimination best-fit equation showing how x-variables matter What is general about GLM? • categorical or continuous x-variables • main effects and interactions • any number of x-variables and interactions

What lies beyond? General Linear Model How is GLM not general? • • • linearity/additivity Normality homogeneity of variance independence a single y-variable

What lies beyond? Generalised Linear Model The Generalised Linear Model relaxes • • • linearity/additivity Normality homogeneity of variance independence a single y-variable

What lies beyond? Generalised Linear Model The Generalised Linear Model adds • link function • variance function • choice for estimating or setting the ‘scale factor’

What lies beyond? Generalised Linear Model The Generalised Linear Model includes: Link function Variance Function Name of model Identity Logit Log Inverse Normal Binomial Poisson Exponential GLM Logistic Regression Log-linear models Survival analyses

What lies beyond? General Linear Model How is GLM not general? • • • linearity/additivity Normality homogeneity of variance independence a single y-variable

What lies beyond? Generalised Linear Model What does Generalised Linear Model do for us? • • partitioning of deviance and DF tests for whether x-variables matter statistical elimination best-fit equation showing how x-variables matter What is general about Generalised Linear Model? • categorical or continuous x-variables • main effects and interactions • any number of x-variables and interactions

What lies beyond? General Linear Model How is GLM not general? • • • linearity/additivity Normality homogeneity of variance independence a single y-variable

What lies beyond? General Linear Model How is GLM not general? • • • linearity/additivity Normality homogeneity of variance independence a single y-variable

What lies beyond? Multivariate methods • • • Principle components analysis Factor analysis Discriminant analysis MANOVA Cluster analysis / Numerical taxonomy

10. 2 (principles of marginality), 10. 4 (applications of marginality), 11. 1 (calculate R 2 or R 2 adj), 5. 3 (orthogonality)

9 (assumptions and model criticism)

9 (assumptions and model criticism)

4 (statistical elimination) 10. 2 (marginality and types of SS) and 10. 4 (examples)

4 (statistical elimination, legs example)

What lies beyond? Last last words… • Learn GLMs for the Biology course and finals • Be prepared to learn Generalised Linear Models for more advanced problems • A chance to do an exam question in the practicals