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Quantitative Methods

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?.

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Quantitative Methods

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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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