Theoretical and empirical review of multinomial process tree modeling

Abstract

We review a current and popular class of cognitive models called multinomial processing tree (MPT) models. MPTmodels are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. Weformally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPTmodels to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPTmodels, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.This article presents a detailed review of a current and popular class of cognitive models called multinomial processing tree (MPT) models. MPT models have been described formally in Riefer and Batchelder (1988) and in Hu and Batchelder (1994b), although models of this type have been around well before the class was first formalized in 1988 (e.g., Batchelder & Riefer, 1980;Chechile & Meyer, 1976;Greeno, James, DaPolito, & Polson, 1978;Humphreys & Bowyer, 1980;B. H. Ross & Bower, 1981). However, the last 10 years have witnessed a deeper understanding and an accelerated use of these models within psychology. This increased popularity of MPT models has resulted not only in the application of these models to new areas in psychology but has also led to a variety of new statistical techniques and a certain amount of theoretical debate. Because of these developments, a review article on this class ofmodels seems timely both for researchers already working in this area and for others who might benefit from using this type of modeling.MPT models are simple, substantively motivated statistical models that can be used to measure underlying or latent cognitive capacities. Psychological data often result from multiple, interacting processes, and operationally 57 defined statistics are quite limited in determining which of these processes are involved in a particular experimental paradigm. One primary use ofMPT models is as dataanalysis tools, capable of disentangling and measuring the separate contribution of different cognitive processes underlying observed data. This approach can be helpful in settling theoretical issues, because psychological theories often focus on one process or another as the fundamental cause of a particular psychological phenomenon. The structural simplicity of the class ofMPT models also makes it a useful framework for developing and testing...

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