Idealizing Reduction: The Microfoundations of Macroeconomics

The dominant view among macroeconomists is that macroeconomics reduces to microeconomics, both in the sense that all macroeconomic phenomena arise out of microeconomic phenomena and in the sense that macroeconomic theory—to the extent that it is correct—can be derived from microeconomic theory. More than that, the dominant view believes that macroeconomics should in practice use the reduced microeconomic theory: this is the program of microfoundations for macroeconomics to which the vast majority of macroeconomists adhere. The “microfoundational” models that they actually employ are, however, characterized by another feature: they are highly idealized, even when they are applied as direct characterizations of actual data, which itself consists of macroeconomic aggregates. This paper explores the interrelationship between reductionism and idealization in the microfoundational program and the role of idealization in empirical modeling.     

Using afterimages for orientation and color to explore mechanisms of visual filling-in

Simulations of Grossberg's FACADE model of visual perception have previously been used to explain afterimage percepts produced by viewing a sequence of orthogonally oriented gratings. Additional simulations of the model are now used to predict new afterimage percepts. One simulation emphasizes that the afterimage percepts are the result of orientation afterresponses and color afterresponses that interact at a filling-in stage. We report experimental data that agree with FACADE's prediction. A second simulation emphasizes the properties of the model's filling-in stage and predicts a situation where the afterimage percept should not appear. We report experimental data indicating that this model prediction is incorrect. We argue that the model is unable to account for this result unless the filling-in stage mechanisms are different from a diffusive-type process. We propose an alternative mechanism, and simulations demonstrate the system's ability to account for the afterimage data.     

How simulations fail

‘The problem with simulations is that they are doomed to succeed.’ So runs a common criticism of simulations—that they can be used to ‘prove’ anything and are thus of little or no scientific value. While this particular objection represents a minority view, especially among those who work with simulations in a scientific context, it raises a difficult question: what standards should we use to differentiate a simulation that fails from one that succeeds? In this paper we build on a structural analysis of simulation developed in previous work to provide an evaluative account of the variety of ways in which simulations do fail. We expand the structural analysis in terms of the relationship between a simulation and its real-world target emphasizing the important role of aspects intended to correspond and also those specifically intended not to correspond to reality. The result is an outline both of the ways in which simulations can fail and the scientific importance of those various forms of failure.     

Generating Race,Gender, and Other Subgroup Data in Personnel Selection Simulations: A pervasive issue with a simple solution

In the past 25 years, organizational researchers and practitioners have relied heavily on computer simulation research to understand how group mean differences and correlations affect overall validity and adverse impact in protected groups (e.g., racial/ethnic groups and gender) as they relate to personnel selection practices. We point out a multilevel issue affecting nearly all past simulations: The total correlations that these simulations intended to specify are somewhat distorted after group mean differences were introduced into the data. Although this distorting effect is minimal in most cases, it matters in some cases, and after all, the main virtue of statistical simulations is precision, both in the population parameters and sample data and statistics those parameters are supposed to generate. We demonstrate this distorting effect through one specific example, based on multiple predictors and meta‐analytic data, followed by a broader simulation for single predictors across a wide variety of selection conditions. Rather than merely point out this problem, we also provide a straightforward solution: multilevel formulas that incorporate both between‐ and within‐group correlations that always correct for this biasing problem, yielding more accurate simulation results. We conclude by discussing applications and promising extensions of this work.     

SIMPOLYCAT: An SAS program for conducting CAT simulation based on polytomous IRT models

A real-data simulation of computerized adaptive testing (CAT) is an important step in real-life CAT applications. Such a simulation allows CAT developers to evaluate important features of the CAT system, such as item selection and stopping rules, before live testing. SIMPOLYCAT, an SAS macro program, was created by the authors to conduct real-data CAT simulations based on polytomous item response theory (IRT) models. In SIMPOLYCAT, item responses can be input from an external file or generated internally on the basis of item parameters provided by users. The program allows users to choose among methods of setting initial ?, approaches to item selection, trait estimators, CAT stopping criteria, polytomous IRT models, and other CAT parameters. In addition, CAT simulation results can be saved easily and used for further study. The purpose of this article is to introduce SIMPOLYCAT, briefly describe the program algorithm and parameters, and provide examples of CAT simulations, using generated and real data. Visual comparisons of the results obtained from the CAT simulations are presented.     

CONSTRUCTING PARALLEL SIMULATION EXERCISES FOR ASSESSMENT CENTERS AND OTHER FORMS OF BEHAVIORAL ASSESSMENT

Assessment centers rely on multiple, carefully constructed behavioral simulation exercises to measure individuals on multiple performance dimensions. Although methods for establishing parallelism among alternate forms of paper-and-pencil tests have been well researched (i.e., to equate tests on difficulty such that the scores can be compared), little research has considered the why and how of parallel simulation exercises. This paper extends established procedures for constructing parallel test forms to dimension-based behavioral simulations. We discuss reasons for establishing comparable, alternate simulation forms and discuss the issues raised when applying traditional procedures to simulation exercises. After proposing a set of guidelines for establishing alternate forms among simulations, we apply these guidelines to simulations used in an operational assessment center.     

A multiple-valued logic approach to the design and verification of hardware circuits

We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are performed in the more informative MVL setting reveal details which are either invisible or harder to detect through binary or ternary simulations. In equivalence verification, detecting different behavior under MVL simulations may lead to the discovery of a genuine binary non-equivalence or to a qualitative gap between two designs. The value of a variable in a simulation may hold information about its degree of truth and its “place of birth” and “date of birth”. Applications include equivalence verification, initialization, assertions generation and verification, partial control on the flow of data by prioritizing and block-oriented simulations. Much of the paper is devoted to theoretical aspects behind the MVL approach, including the reason for choosing a specific algebra for computations and the introduction of the notions of De Morgan Canonical Form and of verification complexity of Boolean expressions. Two basic simulation-based algorithms are presented, one for satisfying and verifying combinational designs and the other for equivalence verification of sequential designs.     

Rigorous results,cross-model justification,and the transfer of empirical warrant: the case of many-body models in physics

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation.     

Phase-oscillator computations as neural models of stimulus–response conditioning and response selection

The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto’s equations. In this article, we build such neural-oscillator models, partly based on neurophysiological evidence, to represent approximately the learning behavior predicted and confirmed in three experiments by well-known stochastic learning models of behavioral stimulus–response theory. We use three Kuramoto oscillators to model a continuum of responses, and we provide detailed numerical simulations and analysis of the three-oscillator Kuramoto problem, including an analysis of the stability points for different coupling conditions. We show that the oscillator simulation data are well-matched to the behavioral data of the three experiments.     

On the importance of avoiding shortcuts in applying cognitive models to hierarchical data

Psychological experiments often yield data that are hierarchically structured. A number of popular shortcut strategies in cognitive modeling do not properly accommodate this structure and can result in biased conclusions. To gauge the severity of these biases, we conducted a simulation study for a two-group experiment. We first considered a modeling strategy that ignores the hierarchical data structure. In line with theoretical results, our simulations showed that Bayesian and frequentist methods that rely on this strategy are biased towards the null hypothesis. Secondly, we considered a modeling strategy that takes a two-step approach by first obtaining participant-level estimates from a hierarchical cognitive model and subsequently using these estimates in a follow-up statistical test. Methods that rely on this strategy are biased towards the alternative hypothesis. Only hierarchical models of the multilevel data lead to correct conclusions. Our results are particularly relevant for the use of hierarchical Bayesian parameter estimates in cognitive modeling.     

Projectible predicates in analogue and simulated systems

We investigate the relationship between two approaches to modeling physical systems. On the first approach, simplifying assumptions are made about the level of detail we choose to represent in a computational simulation with an eye toward tractability. On the second approach simpler, analogue physical systems are considered that have more or less well-defined connections to systems of interest that are themselves too difficult to probe experimentally. Our interest here is in the connections between the artifacts of modeling that appear in these two approaches. We begin by outlining an important respect in which the two are essentially dissimilar and then propose a method whereby overcoming that dissimilarity by hand results in usefully analogous behavior. We claim that progress can be made if we think of artifacts as clues to the projectible predicates proper to the models themselves. Our degree of control over the connection between interesting analogue physical systems and their targets arises from determining the projectible predicates in the analogue system through a combination of theory and experiment. To obtain a similar degree of control over the connection between large-scale, distributed simulations of complex systems and their targets we must similarly determine the projectible predicates of the simulations themselves. In general theory will be too intractable to be of use, and so we advocate an experimental program for determining these predicates.

the object of the natural history which I propose is...to give light to the discovery of causes and supply a suckling philosophy with its first food. Francis Bacon, The Great Instauration

     

The Compatibility of the Structure‐and‐Dynamics Argument and Phenomenal Functionalism about Space

Chalmers argues against physicalism using the premise that no truth about consciousness is deducible a priori from purely structural truths, and later defines what it is for a truth to be structural, which turns out to include spatiotemporal truths. But Chalmers then defines spatiotemporal terms by reference to their role in causing spatiotemporal experiences. Stoljar and Ebbers argue that these definitions allow for the trivial falsification of Chalmers premise about structure and consciousness. I show that this result can be avoided by tweaking the relevant premise, and that this tweak is not ad hoc.     

Numerosity discrimination in deep neural networks: Initial competence,developmental refinement and experience statistics

Both humans and non‐human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate ‘number sense’. However, recent simulation work has challenged this view by showing that human‐like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non‐numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain‐general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.     

Comparative syllogism and counterfactual knowledge

Comparative syllogism is a type of scientific reasoning widely used, explicitly or implicitly, for inferences from observations to conclusions about effectiveness, but its philosophical significance has not been fully elaborated or appreciated. In its simplest form, the comparative syllogism derives a conclusion about the effectiveness of a factor (e.g. a treatment or an exposure) on a certain property via an experiment design using a test (experimental) group and a comparison (control) group. Our objective is to show that the comparative syllogism can be understood as encoding a simulation view of counterfactuals, in that counterfactual situations are conceptual constructs that can be correctly simulated by homogeneous comparison groups. In this simulation view, the empirical data from the comparison groups play an evidential role in the evaluation of counterfactuals and in obtaining counterfactual knowledge. We further indicate how successful experimental designs can help us to obtain correct simulations, and thus to bring us to scientifically-empirically based counterfactual knowledge.     

The role and impact of mental simulation in design

Although theories of mental simulations have used different formulations of the premises of ‘thought experiments’, they can be fitted under a minimalist hypothesis stating that mental simulations are run under situations of uncertainty to turn that uncertainty into approximate answers. Three basic assumptions of mental simulations were tested by using naturalistic data from engineering design. Results from the design protocols showed (1) initial representations in mental simulation had higher than base‐rate uncertainty, (2) uncertainty in mental simulations were lowered after simulation runs, (3) resulting representations had more approximations than base‐rate or initial representations. Further, the reference to external representational systems (sketches and prototypes) was examined. It was found that prototypes had fewer technical/functional simulations compared to sketches or unsupported cognition. Although prototypes were associated with more approximation than unsupported cognition, the different external representation categories did not differ in information uncertainty. The results support the minimalist hypothesis of mental simulations. Copyright © 2008 John Wiley & Sons, Ltd.     

From data to phenomena and back again: computer-simulated signatures

This paper draws attention to an increasingly common method of using computer simulations to establish evidential standards in physics. By simulating an actual detection procedure on a computer, physicists produce patterns of data (‘signatures’) that are expected to be observed if a sought-after phenomenon is present. Claims to detect the phenomenon are evaluated by comparing such simulated signatures with actual data. Here I provide a justification for this practice by showing how computer simulations establish the reliability of detection procedures. I argue that this use of computer simulation undermines two fundamental tenets of the Bogen–Woodward account of evidential reasoning. Contrary to Bogen and Woodward’s view, computer-simulated signatures rely on ‘downward’ inferences from phenomena to data. Furthermore, these simulations establish the reliability of experimental setups without physically interacting with the apparatus. I illustrate my claims with a study of the recent detection of the superfluid-to-Mott-insulator phase transition in ultracold atomic gases.     

A production system model for human problem solving

Summary A new production system model was developed for a class of transformation problems, based upon the results of an experiment which evaluated the psychological validity of a noticing order in problem solving. This model specifies how general problem solving heuristics interact with domain knowledge and how possible actions are assembled from externally presented information. The production system may conceptually be divided into three groups: move generation, move evaluation, and move execution productions. The simulation model was evaluated by a second experiment. With a common set of parameter values, good fits were obtained between the predicted and observed data. The significance of individual productions was assessed by running simulations with individual productions deleted. While previous simulations have described subjects' behavior on a single problem, the present model successfully predicted human problem solving in three structurally different problems. The proposed production system thus gives a detailed account of the procedural knowledge that subjects use in transformation problems.     

Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo evaluation of structural equation models within the context of nonnormal data. The new procedure for nonnormal data simulation is theoretically described and also implemented in the widely used R environment. The quality of the method is assessed by Monte Carlo simulations. A 1-sample test on the observed covariance matrix based on the copula methodology is proposed. This new test for evaluating the quality of a simulation is defined through a particular structural model specification and is robust against normality violations.