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Violation of Independence – Part I

  • Alain F. Zuur
  • Elena N. Ieno
  • Neil J. Walker
  • Anatoly A. Saveliev
  • Graham M. Smith
Chapter
Part of the Statistics for Biology and Health book series (SBH)

Abstract

This chapter explains how correlation structures can be added to the linear regression and additive model. The mixed effects models from Chapters 4 and 5 can also be extended with a temporal correlation structure. The title of this chapter contains ‘Part I’, suggesting that there is also a Part II. Indeed, that is the next chapter. In part I, we use regularly spaced time series, whereas in the next chapter, irregular spaced time series, spatial data, and data along an age gradient are analysed. We use a bird time series data set previously analysed in Reed et al. (2007). In the first section, we start with only one species and show how the linear regression model can be extended with a residual temporal correlation structure. In the second section, we use the same approach for a multivariate time series. In Section 6.3, the owl data are used again.

Keywords

Time Series Linear Regression Model Correlation Structure Residual Correlation Multivariate Time Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alain F. Zuur
    • 1
  • Elena N. Ieno
    • 1
  • Neil J. Walker
    • 2
  • Anatoly A. Saveliev
    • 3
  • Graham M. Smith
    • 4
  1. 1.Highland Statistics LtdNewburghUK
  2. 2.Central Science LaboratoryGloucesterUK
  3. 3.Kazan State UniversityKazanRussia
  4. 4.Bath Spa UniversityBathUK

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