Data-Based Selection of an Appropriate Biological Model: The Key to Modern Data Analysis

Selection of an appropriate model as the basis for data analysis is critical for valid inference. Fundamental to this issue is the concept that the datawill only “support” limited inference. A model should have enough structure and parameters to account adequately for the significant variability in the data, otherwise bias in the estimators is likely. However, if the model has too much structure or too many parameters, then precision is unnecessarily lost and “effects” may be inferred that are not justified by the data. A proper model is fully supported by the data, and has enough parameters to avoid bias, but not too many that precision is lost (the Principle of Parsimony) .Thus, for given data, there is a need to choose objectively from among alternative models, each based on biological considerations. Classical model selection has been based on goodness-of-fit tests (which test only against general alternative hypotheses), or between-model tests (e.g., a likelihood ratio test with a specific alternative hypothesis). Model selection based on classical hypothesis testing can be very difficult and has unknown properties (including overall α-levels). Here we suggest use of Akaike’s Information Criterion (AIC) in likelihood contexts, or Mallow’s C p in regression contexts, for the basis of objective model selection. AIC reduces model selection to a one-dimensional optimization problem emphasizing parsimony, seems to perform well in practice, and is simple to compute and interpret. AIC is similar to Mallow’s C p statistic in the setting of linear models fit by least squares; however, AIC is a likelihood-based criterion. Future data analysis through model building and selection should begin with an array of models that seem biologically reasonable. Then, the central problem of data analysis is selection of an appropriate model as the basis for inference. The use of AIC, likelihood, quasilikelihood, and data resampling (such as the bootstrap), provide modern methods to achieve valid inference. An example is provided.