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Things are not Always Linear; Additive Modelling

Part of the Statistics for Biology and Health book series (SBH)

Abstract

In the previous chapter, we looked at linear regression, and although the word linear implies modelling only linear relationships, this is not necessarily the case. A model of the form Y i = α + β 1 × X i + β 2 × X i 2 + ɛ i is a linear regression model, but the relationship between Y i and X i is modelled using a second-order polynomial function. The same holds if an interaction term is used. For example, in Chapter 2, we modelled the biomass of wedge clams as a function of length, month and the interaction between length and month. But a scatterplot between biomass and length may not necessarily show a linear pattern.

Keywords

  • Akaike Information Criterion
  • Linear Regression Model
  • Generalise Additive Model
  • Regression Spline
  • Smoothing Spline

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.

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Notes

  1. 1.

    This is not entirely true as we will see later. The smoothers used in this chapter consist of a series of local regression-type models, which do allow for prediction. We just don’t get one overall equation.

  2. 2.

    Keele (pg. 69, 2008) shows an example in which the fits of two smoothing splines with the same amount of smoothing (λ) are compared; one smoother uses four knots and the other uses sixteen knots; the difference between the curves is minimal.

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Correspondence to Alain F. Zuur .

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Zuur, A.F., Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M. (2009). Things are not Always Linear; Additive Modelling. 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_3

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