Model selection by minimum description length: Lower-bound sample sizes for the Fisher information approximation

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting in an inversion of the correct rank order of complexity terms for competing models in the worst case. As a remedy, we propose a lower-bound $N^{\mathrm{\prime }}$ for the sample size that suffices to preclude such errors. We illustrate the approach using three examples from the family of multinomial processing tree models.