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Unlocking Advanced Analysis: General Linear Model and Beyond

Explore the power of General Linear Model (GLM) and Generalized Linear Model (GLM) with examples, assumptions, and applications. Dive into multivariate methods and prepare for advanced problems in biology courses.

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Unlocking Advanced Analysis: General Linear Model and Beyond

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  1. Quantitative Methods What lies beyond?

  2. 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

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

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

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

  6. What lies beyond? Generalised Linear Model The Generalised Linear Model includes: Link functionVariance FunctionName of model Identity Normal GLM Logit Binomial Logistic Regression Log Poisson Log-linear models Inverse Exponential Survival analyses

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

  8. 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

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

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

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

  12. 10.2 (principles of marginality), 10.4 (applications of marginality), 11.1 (calculate R2 or R2adj), 5.3 (orthogonality)

  13. 9 (assumptions and model criticism)

  14. 9 (assumptions and model criticism)

  15. 4 (statistical elimination) 10.2 (marginality and types of SS) and 10.4 (examples)

  16. 4 (statistical elimination, legs example)

  17. 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

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