### Abstract

1. Ecological count data typically exhibit complexities such as overdispersion and zero-inflation,
and are often weakly associated with a relatively large number of correlated covariates. The use of
an appropriate statistical model for inference is therefore essential. A common selection criteria for
choosing between nested models is the likelihood ratio test (LRT). Widely used alternatives to the
LRT are based on information-theoretic metrics such as the Akaike Information Criterion.
2. It is widely believed that the LRT can only be used to compare the performance of nested
models – i.e. in situations where one model is a special case of another. There are many situations in
which it is important to compare non-nested models, so, if true, this would be a substantial drawback
of using LRTs for model comparison. In reality, however, it is actually possible to use the
LRT for comparing both nested and non-nested models. This fact is well-established in the statistical
literature, but not widely used in ecological studies.
3. The main obstacle to the use of the LRT with non-nested models has, until relatively recently,
been the fact that it is difficult to explicitly write down a formula for the distribution of the LRT
statistic under the null hypothesis that one of the models is true. With modern computing power it
is possible to overcome this difficulty by using a simulation-based approach.
4. To demonstrate the practical application of the LRT to both nested and non-nested model comparisons,
a case study involving data on questing tick (Ixodes ricinus) abundance is presented. These
data contain complexities typical in ecological analyses, such as zero-inflation and overdispersion,
for which comparison between models of differing structure – e.g. non-nested models – is of particular
importance.
5. Choosingbetweencompeting statisticalmodels isanessentialpartof any appliedecological analysis.
TheLRTis a standard statistical test for comparing nestedmodels. By use of simulation theLRT
can also be used in an analogous fashion to compare non-nested models, thereby providing a unified
approachformodel comparisonwithinthenullhypothesis testingparadigm.Asimple practicalguide
is provided inhowto apply thisapproach to the keymodels required in the analyses of countdata.

Original language | English |
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Pages (from-to) | 155 - 162 |

Number of pages | 8 |

Journal | Methods in Ecology and Evolution |

Volume | 2 |

Issue number | 2 |

Publication status | First published - 2010 |

### Bibliographical note

66060001### Keywords

- Information theoretic metrics
- Model selection
- Non-nested models

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## Cite this

Lewis, F., Butler, A., & Gilbert, L. (2010). A unified approach to model selection using the likelihood ratio test.

*Methods in Ecology and Evolution*,*2*(2), 155 - 162.