  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.
