quantitative methods

Quantitative Methods

What lies beyond?

What lies beyond?

General Linear Model

• categorical or continuous x-variables• main effects and interactions• any number of x-variables and interactions

• 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?

What does GLM do for us?

What lies beyond?

General Linear Model

• linearity/additivity• Normality• homogeneity of variance• independence• a single y-variable

How is GLM not general?

What lies beyond?

Generalised Linear Model

• linearity/additivity• Normality• homogeneity of variance• independence• a single y-variable

The Generalised Linear Model relaxes

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 Normal GLMLogit Binomial Logistic RegressionLog Poisson Log-linear modelsInverse Exponential Survival analyses

What lies beyond?

General Linear Model

• linearity/additivity• Normality• homogeneity of variance• independence• a single y-variable

How is GLM not general?

What lies beyond?

Generalised Linear Model

• categorical or continuous x-variables• main effects and interactions• any number of x-variables and interactions

• 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?

What does Generalised Linear Model do for us?

What lies beyond?

General Linear Model

• linearity/additivity• Normality• homogeneity of variance• independence• a single y-variable

How is GLM not general?

What lies beyond?

General Linear Model

• linearity/additivity• Normality• homogeneity of variance• independence• a single y-variable

How is GLM not general?

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 R2 or R2

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)

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

What lies beyond?