A unified approach to model selection using the likelihood ratio test

Abstract

Summary1. 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. Choosing between competing statistical models is an essential part of any applied ecological analysis. The LRT is a standard statistical test for comparing nested models. By use of simulation the LRT can also be used in an analogous fashion to compare non‐nested models, thereby providing a unified approach for model comparison within the null hypothesis testing paradigm. A simple practical guide is provided in how to apply this approach to the key models required in the analyses of count data.