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Understanding Intuitive Generalized Linear Models and ANOVA Interaction Effects

This document provides a comprehensive overview of Intuitive Generalized Linear Models (GLM) and the application of ANOVA in understanding interaction effects. It dissects the sums of squares associated with various factors—including rows, columns, and interactions—while explaining the partitioning of the total sum of squares. Detailed equations illustrate the relationships among different variables, contributing to a clearer understanding of variance in data analysis. Experts and students alike will find valuable insights into statistical modeling and interpretation.

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Understanding Intuitive Generalized Linear Models and ANOVA Interaction Effects

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  1. Intuitive GLM

  2. ANOVA

  3. (Xijk – Xij.) + (Xi.. – X...) + (X.j. – X...) + (Xij. -Xi.. - X.j. + X…) Eijk + Ri.. + C.j. + Iij. (Xijk – X…) = Ri.. + C.j. + Iij. + Eijk

  4. Iij. = (Xij. - Xi.. - X.j. + X…) = Xij. – [(Xi.. – X…) + (X.j. – X…) + X…] Interaction = Iij.= Xij. – [Di.. + D.j. + X…] Interaction

  5. SS= sum [ (Xijk – Xij.) + (Xi.. – X...) + (X.j. – X...) + (Xi.. + X.j. – Xij. – X…)]2 SStotal = SSerror + SSrows + SScolumns + SSinteraction SS= sum(Xijk – X…)2

  6. SScolumns

  7. SSrows

  8. SSinteraction

  9. SSerror

  10. Partition of Sum of Squares

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