**Path modeling in linear networks**

In many areas of applied sciences and in industrial applications it is known how data blocks are related in time or sequence. It can be instructive to model the data according to this known sequence of the data blocks. There have been developed a large collection of methods to handle this situation. For a review of some introductory analysis see an example.

*Topics*

1. | Introduction. Subdivision of data. |

2. | Graphic display of interconnections. |

3. | Measures of relationships |

4. | The H-method of estimation. One and two data blocks |

5. | Three data blocks |

6. | Case study |

7. | Correlation and prediction |

8. | Simple paths |

9. | Examples |

10. | Comparison of methods |

11. | Network of data blocks |

12. |
Vectors computed (W, T,
P, R)_{i} |

13. | Regressions among data blocks |

14. | Several input (exogenous) and output (endogenous) data blocks |

15. | Multiple objectives |

16. | Comparisons with overall models |

17. | Confidence intervals |

18. | Detection of special features |

19. | Sensitivity analysis |

20. | Case study |

21. | Guidelines for presentation of results |

There are two types of approach that
are of importance. They are correlation and regression approaches. They are
illustrated in the figure below. Consider the case of correlation. If there are
two blocks, we are looking for latent variables
**h**_{1}=**X**_{1}**w**_{1}
and
**h**_{2}=**X**_{2}**w**_{2}
such that latent variables have maximal correlation. In the case of three data
bocks, we are looking for three latent variables,
**h**_{1}**, h**_{2}**, h**_{3},
such that their correlation is as
'large' as possible.

In the case of regression approach the search is
for a score matrix **T**_{1} such that the samples of **T**_{1}
provide with as good prediction of samples of **X**_{2} as possible.

In the case of three data blocks, **
X**_{i}, i=1,2 and 3, we are looking for a score matrix **T**_{1}
and score matrix **T**_{2}, such that if we know a new sample of **X**_{1},
**x**_{10}, we can estimate samples of **X**_{2} and **X**_{3},
**x**_{20} and **x**_{30}, as well as possible. For
instance, such that a prediction of **x**_{30} is as precise as
possible.

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