Bayes factors for the linear ballistic accumulator model of decision-making

Evidence accumulation models of decision-making have led to advances in several different areas of psychology. These models provide a way to integrate response time and accuracy data, and to describe performance in terms of latent cognitive processes. Testing important psychological hypotheses using cognitive models requires a method to make inferences about different versions of the models which assume different parameters to cause observed effects. The task of model-based inference using noisy data is difficult, and has proven especially problematic with current model selection methods based on parameter estimation. We provide a method for computing Bayes factors through Monte-Carlo integration for the linear ballistic accumulator (LBA; Brown and Heathcote, 2008), a widely used evidence accumulation model. Bayes factors are used frequently for inference with simpler statistical models, and they do not require parameter estimation. In order to overcome the computational burden of estimating Bayes factors via brute force integration, we exploit general purpose graphical processing units; we provide free code for this. This approach allows estimation of Bayes factors via Monte-Carlo integration within a practical time frame. We demonstrate the method using both simulated and real data. We investigate the stability of the Monte-Carlo approximation, and the LBA’s inferential properties, in simulation studies.     

Binary recursive partitioning: Background,methods, and application to psychology

Binary recursive partitioning (BRP) is a computationally intensive statistical method that can be used in situations where linear models are often used. Instead of imposing many assumptions to arrive at a tractable statistical model, BRP simply seeks to accurately predict a response variable based on values of predictor variables. The method outputs a decision tree depicting the predictor variables that were related to the response variable, along with the nature of the variables' relationships. No significance tests are involved, and the tree's ‘goodness’ is judged based on its predictive accuracy. In this paper, we describe BRP methods in a detailed manner and illustrate their use in psychological research. We also provide R code for carrying out the methods.     

The simplest complete model of choice response time: linear ballistic accumulation

We propose a linear ballistic accumulator (LBA) model of decision making and reaction time. The LBA is simpler than other models of choice response time, with independent accumulators that race towards a common response threshold. Activity in the accumulators increases in a linear and deterministic manner. The simplicity of the model allows complete analytic solutions for choices between any number of alternatives. These solutions (and freely-available computer code) make the model easy to apply to both binary and multiple choice situations. Using data from five previously published experiments, we demonstrate that the LBA model successfully accommodates empirical phenomena from binary and multiple choice tasks that have proven difficult for other theoretical accounts. Our results are encouraging in a field beset by the tradeoff between complexity and completeness.     

Purely relative models cannot provide a general account of absolute identification

Unidimensional absolute identificatio—identifying a presented stimulus from an ordered set—is a common component of everyday tasks. Laboratory investigations have mostly used equally spaced stimuli, and the theoretical debate has focused on the merits of purely relative versus purely absolute models. Absolute models incorporate substantial knowledge of the complete set of stimuli, whereas relative models allow only partial knowledge and assume that each stimulus is compared with recently observed stimuli. We test and refute a general prediction made by relative models, that accuracy is very low for some stimulus sequences when the stimuli are unequally spaced. We conclude that, although relative judgment processes may occur in absolute identification, a model must incorporate long-term referents to explain performance with unequally spaced stimuli. This implies that purely relative models cannot provide a general account of absolute identification.     

Cancer Survivors’ Spiritual Well-Being and Use of Complementary Methods: A Report from the American Cancer Society’s Studies of Cancer Survivors

We examined associations between spiritual well-being and CAM use among 4,139 cancer survivors. We also explored the classification of religious/spiritual practices (R/S) as CAMs and alternative subscale structures of the Functional Assessment of Chronic Illness Therapy—Spiritual Well-being (FACIT-Sp). We evaluated three aspects of spirituality, Faith, Peace, and Meaning, and use of 19 CAMs in 5 domains. Mind–body methods were subdivided into R/S and non-R/S. All FACIT-Sp factors were associated with CAM use, but in different directions: Meaning and Faith were positively associated; Peace was negatively associated. Peace was negatively associated with R/S CAMs, but not non-R/S CAMs. The prevalence of CAM use dropped from 79.3 to 64.8% when R/S items were excluded. These findings confirm an association between spiritual well-being and CAM use, including some non-R/S CAMs, and provide evidence of the benefits of using the three-factor FACIT-Sp solution and treating R/S CAMs as a separate category.     

Determining the point of subjective ambiguity of ambiguous biological-motion figures with perspective cues

Orthographic frontal/back projections of biological-motion figures are bistable: The point-light figure in principle can be perceived either as facing toward the viewer or as facing away from the viewer. Some point-light actions—for example, walking—elicit a strong “facing bias”: Despite the absence of objective cues to depth, observers tend to interpret the figure as facing toward the viewer in most of the cases. In this article, we present and experimentally validate a technique that affords full experimental control of the perceived in-depth orientation of point-light figures. We demonstrate that by parametrically manipulating the amount of perspective information in the stimulus, it is possible to obtain any desired level of subjective ambiguity. Directions for future research, in which this technique can be fruitfully implemented, are suggested. Program code of a demo is provided that can be modified easily for program code of new experiments. The demo and QuickTime movie files illustrating our perspective manipulation technique may be downloaded from http://brm.psychonomic-journals.org/ content/supplemental.     

The conceptual basis of function learning and extrapolation: Comparison of rule-based and associative-based models

The purpose of this article is to provide a foundation for a more formal, systematic, and integrative approach to function learning that parallels the existing progress in category learning. First, we note limitations of existing formal theories. Next, we develop several potential formal models of function learning, which include expansion of classic rule-based approaches and associative-based models. We specify for the first time psychologically based learning mechanisms for the rule models. We then present new, rigorous tests of these competing models that take into account order of difficulty for learning different function forms and extrapolation performance. Critically, detailed learning performance was also used to conduct the model evaluations. The results favor a hybrid model that combines associative learning of trained input—prediction pairs with a rule-based output response for extrapolation (EXAM).     

Ethical Issues in Engineering Models: An Operations Researcher’s Reflections

This article starts with an overview of the author’s personal involvement—as an Operations Research consultant—in several engineering case-studies that may raise ethical questions; e.g., case-studies on nuclear waste, water management, sustainable ecology, military tactics, and animal welfare. All these case studies employ computer simulation models. In general, models are meant to solve practical problems, which may have ethical implications for the various stakeholders; namely, the modelers, the clients, and the public at large. The article further presents an overview of codes of ethics in a variety of disciples. It discusses the role of mathematical models, focusing on the validation of these models’ assumptions. Documentation of these model assumptions needs special attention. Some ethical norms and values may be quantified through the model’s multiple performance measures, which might be optimized. The uncertainty about the validity of the model leads to risk or uncertainty analysis and to a search for robust models. Ethical questions may be pressing in military models, including war games. However, computer games and the related experimental economics may also provide a special tool to study ethical issues. Finally, the article briefly discusses whistleblowing. Its many references to publications and websites enable further study of ethical issues in modeling.     

Analysis of systems influencing renal hemodynamics and sodium excretion. I. Biochemical systems theory

In this article we present a new methodology—Biochemical Systems Theory and Analysis—as an alternative to traditional parametric statistical procedures for investigating differences between risk groups in a population. We review the systems theory and how it can be used to represent a model of processes influencing renal hemodynamics and sodium (Na⁺) excretion. We also discuss the potential for new measures of the biology of common diseases that can emerge from a synergism between systems theory and population-based statistical approaches. This work was supported in part by grants from the Public Health Service, RO1-HL30428, R01-HL39107 and General Clinical Research Center Grant RR0585.     

Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n×1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a full-rank predictor correlation matrix, R _xx, of order n, and for regression models with constant R ² (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an n-dimensional ellipsoid. The population performance of alternate regression weights—such as equal weights, correlation weights, or rounded weights—can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of R ². To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an n-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in ℝ ⁿ , and (3) populating the set of regression vectors that have constant cosine with a target vector in ℝ ⁿ . Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.     

The Metaphysics of Causal Models

This paper presents an attempt to integrate theories of causal processes—of the kind developed by Wesley Salmon and Phil Dowe—into a theory of causal models using Bayesian networks. We suggest that arcs in causal models must correspond to possible causal processes. Moreover, we suggest that when processes are rendered physically impossible by what occurs on distinct paths, the original model must be restricted by removing the relevant arc. These two techniques suffice to explain cases of late pre?mption and other cases that have proved problematic for causal models.

Jumping to conclusions: A network model predicts schizophrenic patients’ performance on a probabilistic reasoning task

This article extends computational models of schizophrenia that focus on the negative aspects of this syndrome to behavioral biases that are associated with a positive symptom of schizophrenia, namely delusions. The phenomenon studied is the “jump-to-conclusions” style of reasoning that is characterized by delusional patients—in comparison with controls—whereby they make less-informed decisions when an option to collect more decision-specific information is available. Simulations show that these differences can be mimicked by modulating the gain parameter—associated with variations in dopamine level—in a simple network model.     

MISSing the World. Models as Isolations and Credible Surrogate Systems

This article shows how the MISS account of models—as isolations and surrogate systems—accommodates and elaborates Sugden’s account of models as credible worlds and Hausman’s account of models as explorations. Theoretical models typically isolate by means of idealization, and they are representatives of some target system, which prompts issues of resemblance between the two to arise. Models as representations are constrained both ontologically (by their targets) and pragmatically (by the purposes and audiences of the modeller), and these relations are coordinated by a model commentary. Surrogate models are often about single mechanisms. They are distinguishable from substitute models, which are examined without any concern about their connections with the target. Models as credible worlds are surrogate models that are believed to provide access to their targets on account of their credibility (of which a few senses are distinguished).     

The essential process in a family of measurement models

Five members of the Rasch family of latent trait models which have appeared more or less independently in the literature are brought together and identified as one model. In addition to sharing the distinguishing characteristic of the dichotomous Rasch model—separable person and item parameters and hence sufficient statistics—all five models share a common algebraic form and have as their basic element the fundamental process defined by Rasch's simple logistic expression. In these models, the sufficient statistics for person and item parameters are counts of events constructed to be indicative of the variable being measured, and the measures they enable are ‘fundamental’.     

Models of Clergy Spouse Involvement in Protestant Christian Congregations

While all adults in the paid labor force face the difficult task of managing the competing pressures of work and family life, clergy families encounter an added dynamic in the way spouses are integrated into the church. Yet spouses approach involvement in unique and varied ways, making intentional choices over how much or little to participate in the congregations their husbands and wives pastor. Drawing from in-depth interviews with 46 pastors and clergy spouses in five Protestant Christian denominations, this study describes three models of clergy spouse participation showing the diverse ways women and men interpret and enact their role through the ongoing management of boundaries. I consider several social factors informing the model a clergy spouse embraces—pressure from congregants or one’s own ideas, congregational precedent, gender and stage in the life cycle—shedding light on the interaction between individual preferences and contextual factors. In doing so, I argue that although the women and men in this study are continually recreating what it means to be a clergy spouse, they remain heavily rooted in a traditional expectation that pastors’ wives and husbands provide support to their spouse’s church and calling to pastoral ministry.     

Quantile maximum likelihood estimation of response time distributions

Queen’s University, Kingston, Ontario, Canada We introduce and evaluate via a Monte Carlo study a robust new estimation technique that fits distribution functions to grouped response time (RT) data, where the grouping is determined by sample quantiles. The new estimator, quantile maximum likelihood (QML), is more efficient and less biased than the best alternative estimation technique when fitting the commonly used ex-Gaussian distribution. Limitations of the Monte Carlo results are discussed and guidance provided for the practical application of the new technique. Because QML estimation can be computationally costly, we make fast open source code for fitting available that can be easily modified     

Cognitive modeling with spreadsheets

Spreadsheet implementations of two different types of cognitive models—a neural network model and a statistical model—are presented. The two examples illustrate how to employ the facilities of spreadsheets, the spreadsheet data structure, array functions, the built-in function library, and the integrated optimizer, for building cognitive models. The two presented models are new extensions of existing models. They are used for simulating data from experiments illustrating that the extended versions are able to explain experimental results that could not be simulated by the original models. The whole simulation study demonstrates that spreadsheets are a handy tool, especially for researchers without programming knowledge who want to build cognitive models and for instructors teaching cognitive modeling.     

How Truth Behaves When There’s No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixed-point theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.