Mark Pitt
(pitt.2@osu.edu)
Jay Myung (myung.1@osu.edu)
As cognitive modeling continues to grow
in popularity, it is
important that cognitive psychologists in general and future modelers
in particular, entertain this question. Answers are difficult to come
by in the literature. Equally scarce are discussions of why one style
of modeling might be chosen over another (mathematical vs.
connectionist). The purpose of this symposium is to stimulate public
discourse on the topic by having researchers familiar with both
modeling and experimentation present their views, thereby
highlighting the similarities and differences between styles of
modeling. Three researchers (Shiffrin, Plaut, Batchelder) will provide
answers to a common set of questions in the context of
their style of modeling:
Two others (Logan, Wallsten) will then comment on the talks and provide a broader perspective on the enterprise of cognitive modeling.
Psychology's unique place in the sciences, with noisy data
describing almost infinitely complex systems and with ambiguous
explanatory validation, requires modeling but makes it as much an art
as a science. I will discuss levels of explanation, from heuristic de-
scriptions to quantitative fits of data to prescriptive normative
theory, the range in precision of data to be explained, the importance
and im- precision of the qualitative/quantitative distinction and its
implemen tation in modeling, the uses of computational and analytic
methods, methods of model validation and testing, a priori prediction
versus de- scriptive fitting, factors affecting model assessment
including simplicity, elegance, fit, and predictive power, model
evolution and rejection, and uses and misuses of modeling. If time
permits, I will illustrate with examples from (mostly) my own research.
Computational models are often viewed as monolithic theoretical
pro posals that stand or fall as a whole, typically based on the
quantitative match between the model's performance and empirical data.
An alternative, incremental perspective views modeling as more akin to
hypothesis testing. Here, the goal is broader-to explore the
implications of core aspects of a theory by examining how, when
instantiated in specific implementations, they give rise to key
empirical phenomena. A given model is not intended to account for all
aspects of the data and may not include all relevant principles if some
are not critical to the phenomena at hand. Theoretical consistency
across models is encouraged by drawing on a common, coherent set of
computational principles and by gradually expanding the breadth of
empirical coverage of individual models as the implications of the
underlying principles become better understood. The advantages and
pitfalls of this approach will be illustrated by examining
connectionist modeling of reading and language.
Multinomial processing tree (MPT) models are for paradigms
involving categorical data. Parameters are interpreted as probabilities
of hypothesized la- tent cognitive acts during response production-for
example, storing an item in memory, detecting the source of a fact, or
making a particular logical inference. MPT models are paradigm
specific, inten- tionally simple, and validated for specific
experimental conditions. The goal is to measure (estimate ) the latent
parameters and compare them between experimental groups. MPT models are
surely wrong in detail, but their simplicity permits a deep
understanding of their statistical properties: issues in Bayesian and
classical inference, modeling individual differences, and in model
selection. The approach makes no claim to represent deep cognitive
theory; however, when applicable, an MPT model may be more useful than
off-the-shelf statistical packages in understanding data. Thus, MPT
models comprise a cog- nitive psychometrics rather than a cognitive
theory.
Skinner said that science progressed from prediction to
understanding to control. Models plays central role in all three steps.
Models expose the causal forces that underlie phenomena and allow us to
measure aspects of phenomena that cannot be seen directly. This
understanding of the causal forces affords prediction in two senses: It
allows quantitative accounts of existing data, and it suggests
hypotheses about undiscovered aspects of the phenomena, providing a
principled way to extend our knowledge. Understanding and prediction
allow us to control phenomena in laboratory experiments and applied
settings and fosters the development of new theory and the de-
velopment of technology. I will illustrate these ideas with examples
from models of attention, skill acquisition, and executive control.
Under the assumption that models are at best under-dimensionalized representations of reality, the proper question to ask is not whether they are right or wrong (they are always wrong in detail), but whether they are useful. For example, models are useful when they reexpress the data in terms of theoretically meaningful constructs, when they offer insight as to how measurement may take place, or when they systematically misfit the data in ways that lead to new understanding. I will discuss the other presentations from this perspective.