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

Abstract

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.

On the ability to inhibit thought and action: General and special theories of an act of control.

“…At this scale, the failure to predict error RT distributions does not look very substantial. We also tried fitting the data with a version of the linear ballistic accumulator model, which has fit error RT distributions successfully (Brown & Heathcote, 2008). The model assumed each runner involved a linear increase to a threshold, and the slope of the linear increase for each runner was drawn from a normal distribution with a mean of i and a standard deviation of 1.0.…”

“…Many special race models are possible within these constraints, with different assumptions about the stochastic accumulators for each runner. We tried a Poisson counter model (Van Zandt, 2000b) and the linear ballistic accumulator model (Brown & Heathcote, 2008), but we focused on a diffusion to a single threshold. We hope to explore other alternatives.…”

A Dynamic Approach to Recognition Memory

“…The dynamic approach to recognition memory that we adopt (introduced in has its roots in a variety of modern approaches to the dynamics of decision making (Ratcliff, 1978;S. Brown & Heathcote, 2008) and categorization (Nosofsky & Palmeri, 1997;Lamberts, 2000), and reflects a recent trend toward developing models of the timecourse of recognition memory (Brockdorff & Lamberts, 2000;Nosofsky et al, 2011).…”

“…The diffusion model was fit using the same QML procedure we used to fit our model, using the algorithms described by Tuerlincx (2004) to compute the joint accuracy-RT distribution functions and quantiles of the diffusion model. While other models of joint accuracy and RT (e.g., S. Brown & Heathcote, 2008) would likely have sufficed for comparison purposes, we selected a diffusion model for its demonstrated ability to fit a wide variety of data and for its resemblance to our own model, which is also a type of random walk, making it easier to align parameters with a similar function in each model.…”

Parallel interactive retrieval of item and associative information from event memory

“…In addition, while SFT provides strong evidence of interactions between item and associative information, it cannot easily answer question 1b, namely, whether interactions occur during retrieval or are a byproduct of how item and associative information are stored in memory, or both. To address these issues and answer this outstanding question, we augment our SFT analysis by jointly modeling accuracy and response time for each individual within a Linear Ballistic Accumulator (LBA) framework (Brown & Heathcote, 2008). LBA models have been useful for corroborating conclusions derived from SFT (Eidels et al, 2010;Donkin et al, 2014) and have the advantage of jointly modeling both accuracy and response time for both correct and error responses 5 .…”