Posts in Category: analysis

theoretical, mathematical or formal analysis

Paper: Perspectives on the 2×2 Matrix

The 2x2 matrix lens model: Pipeline of perspectives

Hansjörg Neth, Nico Gradwohl, Dirk Streeb, Daniel A. Keim, Wolfgang Gaissmaier

Perspectives on the 2×2 matrix: Solving semantically distinct problems based on a shared structure of binary contingencies

Abstract

Cognition is both empowered and limited by representations.  The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. 
The shared structural construct of a 2×2 matrix supports a set of generic tasks and semantic mappings that provide a tasks, the model links several problems and semantic domains and provides a new unifying framework for understanding problems and defining scientific measures.  Our model’s key explanatory mechanism is the adoption of particular perspectives on a 2×2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization.  As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation. 
To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework.  A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications.

Why read this paper?

This paper is quite long and covers a wide array of concepts and topics.  So what can you expect to gain from reading it?

Paper: FFTrees: An R toolbox to create, visualize, and evaluate FFTs

If a decision tree that measures up very well on the performance criterion
is nevertheless totally incomprehensible to a human expert, can it
be described as knowledge? Under the common-sense definition of this term
as material that might be assimilated and used by human beings, it is not…

J. Ross Quinlan (1987), p. 498

 

 

 

 

Nathaniel Phillips, Hansjörg Neth, Jan Woike, Wolfgang Gaissmaier

FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees

An example of an FFT (created by FFTrees) predicting heard disease.

An example of an FFT predicting the risk of having heart disease.

Abstract:  Fast-and-frugal trees (FFTs) are simple algorithms that facilitate efficient and accurate decisions based on limited information. But despite their successful use in many applied domains, there is no widely available toolbox that allows anyone to easily create, visualize, and evaluate FFTs. We fill this gap by introducing the R package FFTrees.

Paper: Rational task analysis (RTA)

Just as a scissors cannot cut paper without two blades,
a theory of thinking and problem solving cannot predict behavior
unless it encompasses both an analysis of the structure of task environments
and an analysis of the limits of rational adaptation to task requirements.
(Newell & Simon, 1972, p. 55)

 

 

 

 


Hansjörg Neth, Chris R. Sims, Wayne D. Gray

Rational task analysis: A methodology to benchmark bounded rationality

Abstract:  How can we study bounded rationality?  We answer this question by proposing rational task analysis (RTA)—a systematic approach that prevents experimental researchers from drawing premature conclusions regarding the (ir-)rationality of agents.  RTA is a methodology and perspective that is anchored in the notion of bounded rationality and aids in the unbiased interpretation of results and the design of more conclusive experimental paradigms. 

Paper: Melioration as rational choice

Maximization (…) is not a general explanatory principle for behavior. (…)
Melioration (…) is the dynamic process controlling allocation of time across response alternatives.
Herrnstein & Vaughan (1980). Melioration and behavioral allocation, p. 143+172


Chris R. Sims, Hansjörg Neth, Robert A. JacobsWayne D. Gray

Melioration as rational choice: Sequential decision making in uncertain environments

Abstract:  Melioration — defined as choosing a lesser, local gain over a greater longer term gain — is a behavioral tendency that people and pigeons share.  As such, the empirical occurrence of meliorating behavior has frequently been interpreted as evidence that the mechanisms of human choice violate the norms of economic rationality.  In some environments, the relationship between actions and outcomes is known. In this case, the rationality of choice behavior can be evaluated in terms of how successfully it maximizes utility given knowledge of the environmental contingencies.  In most complex environments, however, the relationship between actions and future outcomes is uncertain and must be learned from experience.  When the difficulty of this learning challenge is taken into account, it is not evident that melioration represents suboptimal choice behavior.