New Directions in Multinomial Modeling

This special issue provides an overview of recent developments in the specification and use of multinomial processing tree (MPT) models in experimental psychology. MPT models are versatile instruments for the analysis of discrete data, and they have become increasingly popular especially among cognitive psychologists. Formally, MPT models can be regarded as a specific family of models in the more general class of parameterized multinomial or product-multinomial models (e.g., Andersen, 1990; Bishop, Fienberg, & Holland, 1975; Haberman, 1978). That is, MPT models are statistical tools for the analysis of frequency data that arise from a sample of N observations (or from k samples of N₁, …, N _k observations) which fall into a finite number of discrete categories. Moreover, they allow for the specification and statistical test of hypotheses by reducing the probability parameters of the (product-) multinomial distribution to a smaller set of basic parameters. Although MPT models share these general features with the whole class of parameterized multinomial models, they differ from most other families of parameterized multinomial models (e.g., loglinear models or latent class models) in one respect: Each MPT model has been tailored to a specific experimental paradigm in cognitive psychology, so that the parameters of an MPT model have a well-defined meaning in terms of the cognitive processes that are relevant within a given experimental task. As a consequence, the development of MPT models has been closely intertwined with the development of paradigms and theories in cognitive psychology (see Batchelder & Riefer, 1999; Bröder & Meiser, 2007).

This special issue provides an introduction to and overview of the family of MPT models, and it presents new applications in the field of MPT modeling. In the first contribution, Erdfelder et al. (this issue) introduce the family of MPT models using the one-high-threshold model of recognition memory as a classical example, and they outline the typical steps in MPT model analyses. They then turn to reviewing the use of MPT models in cognitive psychology, which has been most prominent in memory research in paradigms such as yes-no recognition and process dissociation, but also extends to various other fields such as research on propositional reasoning, consensus analyses, and implicit attitude measurement. Finally, current statistical developments are discussed, and computer programs for MPT modeling are reviewed.

The next four contributions are original research articles that present novel MPT modeling approaches in different fields of cognitive psychology. The first two articles are concerned with episodic memory; the third article presents a new model for binary choice, and the final article compares two theories of word identification in reading.

Extending previous work, Bellezza (this issue) comparatively evaluates the different models that have been proposed for analyzing data from the experimental process-dissociation paradigm (Jacoby, 1991). In particular, critical assumptions of the dual-process signal detection model (Yonelinas, 1994) and of the source-monitoring model (Buchner, Erdfelder, Steffens, & Martensen, 1997; Steffens, Buchner, Martensen, & Erdfelder, 2000; Yu & Bellezza, 2000) are evaluated by manipulations of guessing bias in two experiments, and the competing models are fitted to the resulting data. The results favor an account of process-dissociation data in terms of a source-monitoring model over an account in terms of the process-dissociation model. This research emphasizes the importance of comparing competing MPT models, and it illustrates the usefulness of such an enterprise in theory testing.

The article by Bröder (this issue) presents and validates a novel experimental paradigm and MPT model for the measurement of source memory in recall. The established pair-clustering model (Batchelder & Riefer, 1980, 1986) is extended to measure source memory in an adapted version of the pair-clustering recall task. Two experiments are reported in which the new model’s parameters are successfully validated. In addition, a stochastic dependency is observed between source recall of the two items of a clustered pair, suggesting that binding of contextual as well as semantic features occurs during clustering, and that source recall follows similar regularities as source recognition (Meiser, Sattler, & Weißer, 2008).

The article by Batchelder, Hu, and Smith (this issue) reviews research on models for binary choice and provides an enlightening discussion of the relations between different psychological models of choice behavior. The article also highlights the similarities and differences between prominent models in choice research and the family of MPT models, and it introduces an MPT model for binary choice in paired-comparison situations. The model is derived from a Markov-chain model that is itself derived from the choice model by Bradley and Terry (1952) and Luce (1959). The article illustrates the application of the choice MPT model using a classical set of data on the preference for vegetables.

The article by Maris and de Graaff Stoffers (this issue) compares single- and dual-process theories of reading, using processing-tree model instantiations of these theories. These models are applied to account for the data from two reading experiments with children. The results clearly favor the dual-route model over the single-route model. This article again illustrates the usefulness of model-based analyses in the comparative testing of theories.

In their discussion of statistical developments of the MPT model family, Erdfelder et al. (this issue) address the issue of parameter heterogeneity, which is a potential threat to the validity of analyses performed on data aggregated across participants. The other authors in this special issue are also sensitive to this issue (e.g., Bröder, this issue; Maris & de Graaff Stoffers, this issue). Recently, hierarchical modeling approaches have become available that allow for parameter heterogeneity between participants or subpopulations of participants (Klauer, 2006; Rouder, Lu, Morey, Sun, & Speckman, 2008; Stahl & Klauer, 2007) and that have proven useful in various applications (e.g., Stahl & Degner, 2007; Stahl & Klauer, 2008).

Beyond their ability to deal with the potential threats of parameter heterogeneity to the validity of traditional analyses, hierarchical modeling approaches have important merits: By integrating participant (and item) heterogeneity into the model using person (and item) parameters, hierarchical cognitive models become similar to psychometric models. Thus, hierarchical MPT models allow one to integrate the tradition of cognitive psychology and the tradition of psychometrics in an approach called cognitive psychometrics: the study of interindividual differences in cognitive processes in fields such as psychological assessment and abnormal psychology (Batchelder, 1998; Riefer, Knapp, Batchelder, Bamber, & Manifold, 2002). The reader will find these issues and many other ongoing developments and extensions of MPT modeling discussed throughout the articles of this special issue, highlighting that MPT modeling remains an active field of research.