Lumped-Parameter Response Time Models for Pneumatic Circuit Dynamics

Resistor–capacitor (RC) response time models for pressurizing and depressurizing a pneumatic capacitor (mass accumulator) through a resistor (flow restriction) comprise a framework to systematically analyze complex fluidic circuits. A model for pneumatic resistance is derived from a combination of fundamental fluid mechanics and experimental results. Models describing compressible fluid capacitance are derived from thermodynamic first principles and validated experimentally. The models are combined to derive the ordinary differential equations that describe the RC dynamics. These equations are solved analytically for rigid capacitors and numerically for deformable capacitors to generate pressure response curves as a function of time. The dynamic pressurization and depressurization response times to reach 63.2% (or 1−e−1) of exponential decay are validated in simple pneumatic circuits with combinations of flow restrictions ranging from 100 μm to 1 mm in diameter, source pressures ranging from 5 to 200 kPa, and capacitor volumes of 0.5 to 16 mL. Our RC models predict the response times, which range from a few milliseconds to multiple seconds depending on the combination, with a coefficient of determination of r2=0.983. The utility of the models is demonstrated in a multicomponent fluidic circuit to find the optimal diameter of tubing between a three-way electromechanical valve and a pneumatic capacitor to minimize the response time for the changing pressure in the capacitor. These lumped-parameter models represent foundational blocks upon which timing models of pneumatic circuits can be built for a variety of applications from soft robotics and industrial automation to high-speed microfluidics.

Assessing Fit of the Lognormal Model for Response Times

Response time models (RTMs) are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular RTMs. Several existing statistics for testing normality and the fit of factor analysis models are repurposed for testing the fit of the lognormal model. A simulation study and two real data examples demonstrate the usefulness of the statistics. The Shapiro–Wilk test of normality and a z-test for factor analysis models were the most powerful in assessing the misfit of the lognormal model.

Fast and accurate calculations for first-passage times in Wiener diffusion models

We propose a new method for quickly calculating the probability density function for first-passage times in simple Wiener diffusion models, extending an earlier method used by [Van Zandt, T., Colonius, H., & Proctor, R. W. (2000). A comparison of two response-time models applied to perceptual matching. Psychonomic Bulletin & Review, 7, 208–256]. The method relies on the observation that there are two distinct infinite series expansions of this probability density, one of which converges quickly for small time values, while the other converges quickly at large time values. By deriving error bounds associated with finite truncation of either expansion, we are able to determine analytically which of the two versions should be applied in any particular context. The bounds indicate that, even for extremely stringent error tolerances, no more than 8 terms are required to calculate the probability density. By making the calculation of this distribution tractable, the goal is to allow more complex extensions of Wiener diffusion models to be developed.

The Quality of Response Time Data Inference: A Blinded, Collaborative Assessment of the Validity of Cognitive Models

Most data analyses rely on models. To complement statistical models, psychologists have developed cognitive models, which translate observed variables into psychologically interesting constructs. Response time models, in particular, assume that response time and accuracy are the observed expression of latent variables including 1) ease of processing, 2) response caution, 3) response bias, and 4) non–decision time. Inferences about these psychological factors, hinge upon the validity of the models’ parameters. Here, we use a blinded, collaborative approach to assess the validity of such model-based inferences. Seventeen teams of researchers analyzed the same 14 data sets. In each of these two–condition data sets, we manipulated properties of participants’ behavior in a two–alternative forced choice task. The contributing teams were blind to the manipulations, and had to infer what aspect of behavior was changed using their method of choice. The contributors chose to employ a variety of models, estimation methods, and inference procedures. Our results show that, although conclusions were similar across different methods, these “modeler’s degrees of freedom” did affect their inferences. Interestingly, many of the simpler approaches yielded as robust and accurate inferences as the more complex methods. We recommend that, in general, cognitive models become a typical analysis tool for response time data. In particular, we argue that the simpler models and procedures are sufficient for standard experimental designs. We finish by outlining situations in which more complicated models and methods may be necessary, and discuss potential pitfalls when interpreting the output from response time models.

An Exemplar-Based Random-Walk Model of Categorization and Recognition

In this chapter, we provide a review of a process-oriented mathematical model of categorization known as the exemplar-based random-walk (EBRW) model (Nosofsky & Palmeri, 1997a). The EBRW model is a member of the class of exemplar models. According to such models, people represent categories by storing individual exemplars of the categories in memory, and classify objects on the basis of their similarity to the stored exemplars. The EBRW model combines ideas ranging from the fields of choice and similarity, to the development of automaticity, to response-time models of evidence accumulation and decision-making. This integrated model explains relations between categorization and other fundamental cognitive processes, including individual-object identification, the development of expertise in tasks of skilled performance, and old-new recognition memory. Furthermore, it provides an account of how categorization and recognition decision-making unfold through time. We also provide comparisons with some other process models of categorization.