Skip to main content

Violation of Independence – Part I

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-387-87458-6_6
  • Chapter length: 18 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-87458-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)
Hardcover Book
USD   149.99
Price excludes VAT (USA)
Fig. 6.1
Fig. 6.2
Fig. 6.3
Fig. 6.4
Fig. 6.5
Fig. 6.6
Fig. 6.7

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alain F. Zuur .

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M. (2009). Violation of Independence – Part I. In: Mixed effects models and extensions in ecology with R. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87458-6_6

Download citation