Model selection by minimum description length: Lower-bound sample sizes for the Fisher information approximation
This work provides a practical solution for researchers using FIA in model selection, though it is incremental as it builds on existing methods.
The paper addresses the issue of the Fisher information approximation (FIA) being misleading in finite samples by proposing a lower-bound sample size to prevent errors in model selection, demonstrating this with examples from multinomial processing tree models.
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 $N'$ 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.