On the minimum description length complexity of multinomial processing tree models

Multinomial processing tree (MPT) modeling is a statistical methodology that has been widely and successfully applied for measuring hypothesized latent cognitive processes in selected experimental paradigms. This paper concerns model complexity of MPT models. Complexity is a key and necessary concept to consider in the evaluation and selection of quantitative models. A complex model with many parameters often overfits data beyond and above the underlying regularities, and therefore, should be appropriately penalized. It has been well established and demonstrated in multiple studies that in addition to the number of parameters, a model’s functional form, which refers to the way by which parameters are combined in the model equation, can also have significant effects on complexity. Given that MPT models vary greatly in their functional forms (tree structures and parameter/category assignments), it would be of interest to evaluate their effects on complexity. Addressing this issue from the minimum description length (MDL) viewpoint, we prove a series of propositions concerning various ways in which functional form contributes to the complexity of MPT models. Computational issues of complexity are also discussed.