**Multiple objectives. Multiple weighing schemes.**

*Topics*

1. | Introduction. Multiple objectives. | |

2. | Analysis of two-way data. | |

3. | Scaling of data. | |

4. | The H-method of estimation. | |

5. | Graphic analysis. | |

6. | Case study | |

7. | Mathematics of multiple weighing schemes. | |

8. | Modelling strategies. | |

9. | Examples | |

10. | Dimension analysis. | |

11. | Regression using multiple weighing schemes. | |

12. | Graphic analysis. | |

13. | Use of weighing schemes in multi-way data. | |

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 |

Traditional statistical analysis of data assumes that data consist of repeated samples. But in applications it may not be natural to look at the data in this way. An example is the experiment of tasting of food samples. There may be given judges that taste on some specific types of food. Neither the judges nor the types of food may be considered as the sample dimension. In the analysis of such data we do not distinguish between role of score and loading vectors. Some optimization procedures are used to find good score vectors and some other optimization procedures to find optimal loading vectors. When these two have been found it is judged how we should proceed with the present step of the analysis. By using these procedures it may be possible to get better description of data than traditional methods give. The disadvantage may be that we do not have the well-known properties of the score and loading vectors, for instance the score vectors may not be orthogonal.

See a short review of some of the mathematical ideas.