Likelihood-Free Algorithms

Theories that describe how people assign prices and make choices are typically based on the idea that both of these responses are derived from a common static, deterministic function used to assign utilities to options. However, preference reversals -where prices assigned to gambles conflict with preference orders elicited through binary choices -indicate that the response processes underlying these different methods of evaluation are more intricate. We address this issue by formulating a new computational model that assumes an initial bias or anchor that depends on type of price task (buying, selling, or certainty equivalents) and a stochastic evaluation accumulation process that depends on gamble attributes. To test this new model, we investigated choices and prices for a wide range of gambles and price tasks, including pricing under time pressure. In line with model predictions, we found that price distributions possessed stark skew that depended on the type of price and the attributes of gambles being considered. Prices were also sensitive to time pressure, indicating a dynamic evaluation process underlying price generation. The model out-performed prospect theory in predicting prices, and additionally predicted the associated response times, which no prior model has accomplished. Finally, we show that the model successfully predicts out-of-sample choices and choice response times. This price accumulation model therefore provides a superior account of the distributional and dynamic properties of price, leveraging process-level mechanisms to provide a more complete account the valuation processes common across multiple methods of eliciting preference.

Section: Model Comparison and Fitmentioning

confidence: 99%

A distributional and dynamic theory of pricing and preference.

Kvam

Busemeyer

2020

“…Instead, we recommend an approach for model fitting based on kernel density estimation to turn the simulated data into a truly continuous, two-dimensional distribution of responses and response times. This method has been effectively used to approximate the likelihoods of several types of simulation-based models (Kvam & Busemeyer, 2020; Palestro et al, 2018; Turner & Sederberg, 2014; Turner & Van Zandt, 2012), is reasonably efficient especially with the addition of signal processing methods (Holmes, 2015; Lin et al, 2019), and can be easily adapted to a two-dimensional joint distribution like the one produced by the SCDM and GSR model. For these models, we can simulate a large number of trials from the model, use the kernel density method to generate an approximate likelihood, and then impute the likelihood of each combination of response and response time in the observed data set.…”

Section: Discussionmentioning

confidence: 99%

Reconciling similarity across models of continuous selections.

Kvam

Turner

2021

Self Cite

Recently-developed models of decision making have provided accounts of the cognitive processes underlying choice on tasks where responses can fall along a continuum, such as identifying the color or orientation of a stimulus. Even though nearly all of these models seek to extend diffusion decision processes to a continuum of response options, they vary in terms of complexity, tractability, and their ability to predict patterns of data such as multimodal distributions of responses. We suggest that these differences are almost entirely due to differences in how these models account for the similarity among response options. In this theoretical note, we reconcile these differences by characterizing the existing models under a common framework, where the assumptions about psychological representations of similarity, and their implications for behavioral data (e.g., multimodal responses), are made explicit. Furthermore, we implement a simulation-based approach to computing model likelihoods that allows for greater freedom in constructing and implementing continuous response models. The resulting geometric similarity representation (GSR) can supplement approaches like the circular / spherical diffusion models by allowing them to generate multimodal distributions of responses from a single drift, or simplify models like the spatially continuous diffusion model by condensing their representations of similarity and allowing them to generate simulations more efficiently. To illustrate its utility, we apply this approach to multimodal distributions responses, twodimensional responses (such as locations on a computer screen), and continuua of response options with nontrivial, nonlinear similarity relations between response options.

“…While the concept of the likelihood function is well-established (see Myung, 2003, for a tutorial), the calculations can be difficult. Alternatively, approximate versions of the likelihood function can be implemented (Palestro et al, 2018).…”

Section: The Likelihood Function For Swiftmentioning

confidence: 99%

“…Finally, for the temporal probability density P temp in Equation (6), exact computation is precluded by the complexity of the cascade of random timers. Here, the probability density can be approximated via kernel density estimation (Epanechnikov, 1969), an approach termed probability density approximation (Holmes, 2015; Palestro et al, 2018; Turner & Sederberg, 2014).…”

Section: The Likelihood Function For Swiftmentioning

confidence: 99%

A Bayesian approach to dynamical modeling of eye-movement control in reading of normal, mirrored, and scrambled texts.

Rabe¹,

Chandra²,

Krügel³

et al. 2021

In eye-movement control during reading, advanced process-oriented models have been developed to reproduce behavioral data. So far, model complexity and large numbers of model parameters prevented rigorous statistical inference and modeling of interindividual differences. Here we propose a Bayesian approach to both problems for one representative computational model of sentence reading (SWIFT; Engbert et al., Psychological Review, 112, 2005, pp. 777-813). We used experimental data from 36 subjects who read text in a normal and one of four manipulated text layouts (e.g., mirrored and scrambled letters). The SWIFT model was fitted to subjects and experimental conditions individually to investigate between-subject variability. Based on posterior distributions of model parameters, fixation probabilities and durations are reliably recovered from simulated data and reproduced for withheld empirical data, at both the experimental condition and subject levels. A subsequent statistical analysis of model parameters across reading conditions generates model-driven explanations for observable effects between conditions.