6. Latent Variable Modelling

• 6.1. In context
  • 6.1.1. What we will cover
• 6.2. References and readings
  • 6.2.1. General
  • 6.2.2. PCA
  • 6.2.3. PLS
• 6.3. Extracting value from data
  • 6.3.1. The types of data engineers deal with now
  • 6.3.2. Issues faced with engineering data
• 6.4. What is a latent variable?
  • 6.4.1. Your health
  • 6.4.2. Room temperature
• 6.5. Principal Component Analysis (PCA)
  • 6.5.1. Visualizing multivariate data
  • 6.5.2. Geometric explanation of PCA
  • 6.5.3. Mathematical derivation for PCA
  • 6.5.4. More about the direction vectors (loadings)
  • 6.5.5. PCA example: Food texture analysis
  • 6.5.6. Interpreting score plots
  • 6.5.7. Interpreting loading plots
  • 6.5.8. Interpreting loadings and scores together
  • 6.5.9. Predicted values for each observation
  • 6.5.10. Interpreting the residuals
  • 6.5.11. PCA example: analysis of spectral data
  • 6.5.12. Hotelling’s T²
  • 6.5.13. Preprocessing the data before building a model
  • 6.5.14. Algorithms to calculate (build) PCA models
  • 6.5.15. Testing the PCA model
  • 6.5.16. Determining the number of components to use in the model with cross-validation
  • 6.5.17. Some properties of PCA models
  • 6.5.18. Latent variable contribution plots
  • 6.5.19. Using indicator variables in a latent variable model
  • 6.5.20. Visualization latent variable models with linking and brushing
  • 6.5.21. PCA Exercises
• 6.6. Principal Component Regression (PCR)
• 6.7. Introduction to Projection to Latent Structures (PLS)
  • 6.7.1. Advantages of the projection to latent structures (PLS) method
  • 6.7.2. A conceptual explanation of PLS
  • 6.7.3. A mathematical/statistical interpretation of PLS
  • 6.7.4. A geometric interpretation of PLS
  • 6.7.5. Interpreting the scores in PLS
  • 6.7.6. Interpreting the loadings in PLS
  • 6.7.7. How the PLS model is calculated
  • 6.7.8. Variability explained with each component
  • 6.7.9. Coefficient plots in PLS
  • 6.7.10. Analysis of designed experiments using PLS models
  • 6.7.11. Using a PLS model backwards: model inversion and the null space
  • 6.7.12. PLS Exercises