Analysis of multi-way data


1. Introduction. Multi-way data.  
2. Analysis of two-way data. 
3. Extensions to multi-way data.
4. The H-method of estimation.
5. Graphic analysis.
6. Case study
7. Mathematics of multi-way data.
8. Modeling strategies.
9. Examples
10. Dimension analysis.
11. Regression using multi-way data.
12. Graphics in regression analysis.
13. Regressions among data blocks
14. Specialized procedures
15. Case study.
16. Comparisons of methods
17. Confidence intervals
18. Detection of special features
19. Sensitivity analysis
20. Case study
21. Guidelines for presentation of results
In applications it is often natural to look at data as being of multi-way type, where each sample of measurements has values of different kinds. These types of data structures provide with a special challenge, because the linear analysis known for two-way data (matrices) does not directly extend to multi-way data. The approach chosen in the methods presented here is to develop algorithms that are based on specific indices of the data values, X=(xij). These algorithms extend naturally to data characterized by many indices, X=(xijkl). The procedures developed reduce to similar well known ones, when data has two indices. This approach provides with natural ways to define generalized inverse and other magnitudes for multi-way data, which are used for two-way data. See a short review of ideas.