An Information Theoretic Approach to Model Selection: A Tutorial with Monte Carlo Confirmation.

A reliance on null hypothesis significance testing (NHST) and misinterpretations of its results are thought to contribute to the replication crisis while impeding the development of a cumulative science. One solution is a data-analytic approach called Information-Theoretic (I-T) Model Selection, which builds upon Maximum Likelihood estimates. In the I-T approach, the scientist examines a set of candidate models and determines for each one the probability that it is the closer to the truth than all others in the set. Although the theoretical development is subtle, the implementation of I-T analysis is straightforward. Models are sorted according to the probability that they are the best in light of the data collected. It encourages the examination of multiple models, something investigators desire and that NHST discourages. This article is structured to address two objectives. The first is to illustrate the application of I-T data analysis to data from a virtual experiment. A noisy delay-discounting data set is generated and seven quantitative models are examined. In the illustration, it is demonstrated that it is not necessary to know the "truth" is to identify the one that is closest to it and that the most likely models conform to the model that generated the data. Second, we examine claims made by advocates of the I-T approach using Monte Carlo simulations in which 10,000 different data sets are generated and analyzed. The simulations showed that 1) the probabilities associated with each model returned by the single virtual experiment approximated those that resulted from the simulations, 2) models that were deemed close to the truth produced the most precise parameter estimates, and 3) adding a single replicate sharpens the ability to identify the most probable model.