Model Assessment Tools for a Model False World

TL;DR

This paper introduces a model credibility index to evaluate how well a model approximates the true data-generating process, acknowledging that most models are inherently false but still useful.

Contribution

It proposes a new credibility index based on the maximum sample size where model and true data are indistinguishable, offering a novel perspective on model adequacy.

Findings

The credibility index can be estimated using data subsampling.

Models are viewed as flawed yet useful despite being false.

The approach extends existing hypothesis testing frameworks.

Abstract

A standard goal of model evaluation and selection is to find a model that approximates the truth well while at the same time is as parsimonious as possible. In this paper we emphasize the point of view that the models under consideration are almost always false, if viewed realistically, and so we should analyze model adequacy from that point of view. We investigate this issue in large samples by looking at a model credibility index, which is designed to serve as a one-number summary measure of model adequacy. We define the index to be the maximum sample size at which samples from the model and those from the true data generating mechanism are nearly indistinguishable. We use standard notions from hypothesis testing to make this definition precise. We use data subsampling to estimate the index. We show that the definition leads us to some new ways of viewing models as flawed but useful. The concept is an extension of the work of Davies [Statist. Neerlandica 49 (1995) 185--245].