Academic journal article Psychonomic Bulletin & Review

Minimum Description Length Model Selection of Multinomial Processing Tree Models

Academic journal article Psychonomic Bulletin & Review

Minimum Description Length Model Selection of Multinomial Processing Tree Models

Article excerpt

Multinomial processing tree (MPT) modeling has been widely and successfully applied as a statistical methodology for measuring hypothesized latent cognitive processes in selected experimental paradigms. In this article, we address the problem of selecting the best MPT model from a set of scientifically plausible MPT models, given observed data. We introduce a minimum description length (MDL) based model-selection approach that overcomes the limitations of existing methods such as the G^sup 2^-based likelihood ratio test, the Akaike information criterion, and the Bayesian information criterion. To help ease the computational burden of implementing MDL, we provide a computer program in MATLAB that performs MDL-based model selection for any MPT model, with or without inequality constraints. Finally, we discuss applications of the MDL approach to well-studied MPT models with real data sets collected in two different experimental paradigms: source monitoring and pair clustering. The aforementioned MATLAB program may be downloaded from http://pbr.psychonomic-journals.org/content/supplemental.

(ProQuest: ... denotes formulae omitted.)

Multinomial processing tree (MPT) modeling is a statistical methodology for measuring latent cognitive capacities in selected experimental paradigms (Batchelder & Riefer, 1986, 1990, 1999; Chechile, 2004; Erdfelder et al., 2009; Hu & Batchelder, 1994; Riefer & Batchelder, 1988, 1991, 1995; Riefer, Hu, & Batchelder, 1994). The data structure requires that participants performing a cognitive task make categorical responses to a series of test items. An MPT model parameterizes a subset of probability distributions over the response categories by specifying a processing tree designed to represent hypothesized cognitive steps, such as memory encoding, storage, discrimination, inference, guessing, and retrieval.

Since its introduction in the 1980s, MPT models have been successfully applied to modeling performance in a wide range of cognitive tasks, including associative recall, source monitoring, eyewitness memory, hindsight bias, object perception, speech perception, propositional reasoning, social networks, and cultural consensus. Batchelder and Riefer (1999) listed over 80 applications of MPT models in various areas of cognitive and social psychology. MPT models have also been applied to estimate cognitive deficits in special populations (Batchelder & Riefer, 2007; Chechile, 2007; see Erdfelder et al., 2009, for a review of such applications). The use of MPT models to assess special populations is often referred to as cognitive psychometrics, representing the fact that theoretically motivated models are employed as measurement tools of cognitive functioning (Batchelder, 2009; Batchelder & Riefer, 2007; Riefer, Knapp, Batchelder, Bamber, & Manifold, 2002). In all of these applications, MPT models were intended to offer researchers more instructive and informative interpretations of data than those based on the traditional data analytic approaches, such as the ANOVA.

In the present study, we are concerned with the logic of selecting the best MPT model from a set of scientifically plausible MPT models that are available to account for a given data set. A researcher may entertain multiple scientific hypotheses about the underlying processes, each formulated as a distinct MPT model,1 and may wish to determine which one of these models best describes the observed data in some defined sense; this is the problem of model selection (Myung & Pitt, 1997). By selecting among theoretically motivated models, the researcher is able to identify from alternative theories the one best supported by empirical observations. To illustrate, consider the question of how the different languages of bilingual people are cognitively represented. Several theories addressing this issue differ as to whether information presented in a particular language retains a language-specific tag. …

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