Multinomial processing tree models: A review of the literature.

Multinomial processing tree (MPT) models have become popular in cognitive psychology in the past two decades. In contrast to general-purpose data analysis techniques, such as log-linear models or other generalized linear models, MPT models are substantively motivated stochastic models for categorical data. They are best described as tools (a) for measuring the cognitive processes that underlie human behavior in various tasks and (b) for testing the psychological assumptions on which these models are based. The present article provides a review of MPT models and their applications in psychology, focusing on recent trends and developments in the past 10 years. Our review is nontechnical in nature and primarily aims at informing readers about the scope and utility of MPT models in different branches of cognitive psychology. In a now classical article, Riefer and Batchelder (1988) proposed a class of substantively motivated stochastic mod- els for categorical behavioral data which was relatively well known in statistical genetics at the time (e.g., Elandt- Johnson, 1971), but had received little attention in psycho- logical research up to the 1980s. These models are now known as multinomial processing tree (MPT) models. About 10 years later, Batchelder and Riefer (1999) already identified no less than 30 published MPT models in the psychological literature, most of which were applied to different agendas in cognitive research. The present article provides an update of Batchelder and Riefer's review and focuses on models and their applications published in the past 10 years. Our review includes 70 MPT models and model variants from more than 20 research areas. In the first section, we will present a brief conceptual outline of MPT models using a simple example to illustrate the basics and main advantages of this approach. Technical details will be omitted almost entirely because they have been described elsewhere (e.g., Batchelder & Riefer, 1999; Hu & Batchelder, 1994). The second section sum- marizes MPT models and their applications in different branches of cognitive psychology, with a special focus on models for various memory paradigms. In the third sec- tion, psychological applications of MPT models outside the realm of cognitive psychology will be briefly summarized. The fourth section describes recent developments, general- izations, and innovations in the statistical methodology of MPT models that might be useful for those interested in applying such models. The fifth and final section of our review provides a sketch of computer programs that are currently available for statistical analyses in the MPT framework, along with a summary of the main advantages of each program.