Plane Answers to Complex Questions: The Theory of Linear Models
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2002
|
| Edition: | Third Edition |
| Series: | Springer Texts in Statistics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The third edition of Plane Answers includes fundamental changes in how some aspects of the theory are handled. Chapter 1 includes a new section that introduces generalized linear models. Primarily, this provides a definition so as to allow comments on how aspects of linear model theory extend to generalized linear models. For years I have been unhappy with the concept of estimability. Just because you cannot get a linear unbiased estimate of something does not mean you cannot estimate it. For example, it is obvious how to estimate the ratio of two contrasts in an ANOVA, just estimate each one and take their ratio. The real issue is that if the model matrix X is not of full rank, the parameters are not identifiable. Section 2.1 now introduces the concept of identifiability and treats estimability as a special case of identifiability. This change also resulted in some minor changes in Section 2.2. In the second edition, Appendix F presented an alternative approach to dealing with linear parametric constraints. In this edition I have used the new approach in Section 3.3. I think that both the new approach and the old approach have virtues, so I have left a fair amount of the old approach intact. Chapter 8 contains a new section with a theoretical discussion of models for factorial treatment structures and the introduction of special models for homologous factors. This is closely related to the changes in Section 3.3 |
| Physical Description: | 1 Online-Ressource (XIX, 476 p) |
| ISBN: | 9780387215440 9781441929716 |
| ISSN: | 1431-875X |
| DOI: | 10.1007/978-0-387-21544-0 |
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| spelling | Christensen, Ronald Verfasser aut Plane Answers to Complex Questions The Theory of Linear Models by Ronald Christensen Third Edition New York, NY Springer New York 2002 1 Online-Ressource (XIX, 476 p) txt rdacontent c rdamedia cr rdacarrier Springer Texts in Statistics 1431-875X The third edition of Plane Answers includes fundamental changes in how some aspects of the theory are handled. Chapter 1 includes a new section that introduces generalized linear models. Primarily, this provides a definition so as to allow comments on how aspects of linear model theory extend to generalized linear models. For years I have been unhappy with the concept of estimability. Just because you cannot get a linear unbiased estimate of something does not mean you cannot estimate it. For example, it is obvious how to estimate the ratio of two contrasts in an ANOVA, just estimate each one and take their ratio. The real issue is that if the model matrix X is not of full rank, the parameters are not identifiable. Section 2.1 now introduces the concept of identifiability and treats estimability as a special case of identifiability. This change also resulted in some minor changes in Section 2.2. In the second edition, Appendix F presented an alternative approach to dealing with linear parametric constraints. In this edition I have used the new approach in Section 3.3. I think that both the new approach and the old approach have virtues, so I have left a fair amount of the old approach intact. Chapter 8 contains a new section with a theoretical discussion of models for factorial treatment structures and the introduction of special models for homologous factors. This is closely related to the changes in Section 3.3 Statistics Mathematical statistics Statistical Theory and Methods Statistik Lineares Modell (DE-588)4134827-8 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Lineares Modell (DE-588)4134827-8 s 2\p DE-604 https://doi.org/10.1007/978-0-387-21544-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Christensen, Ronald Plane Answers to Complex Questions The Theory of Linear Models Statistics Mathematical statistics Statistical Theory and Methods Statistik Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4123623-3 |
| title | Plane Answers to Complex Questions The Theory of Linear Models |
| title_auth | Plane Answers to Complex Questions The Theory of Linear Models |
| title_exact_search | Plane Answers to Complex Questions The Theory of Linear Models |
| title_full | Plane Answers to Complex Questions The Theory of Linear Models by Ronald Christensen |
| title_fullStr | Plane Answers to Complex Questions The Theory of Linear Models by Ronald Christensen |
| title_full_unstemmed | Plane Answers to Complex Questions The Theory of Linear Models by Ronald Christensen |
| title_short | Plane Answers to Complex Questions |
| title_sort | plane answers to complex questions the theory of linear models |
| title_sub | The Theory of Linear Models |
| topic | Statistics Mathematical statistics Statistical Theory and Methods Statistik Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Statistics Mathematical statistics Statistical Theory and Methods Statistik Lineares Modell Lehrbuch |
| url | https://doi.org/10.1007/978-0-387-21544-0 |
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