Parameter estimation in evidence-accumulation models of choice response times is demanding of both the data and the user. We outline how to fit evidence-accumulation models using the flexible, open-source, R-based Dynamic Models of Choice (DMC) software. DMC provides a hands-on introduction to the Bayesian implementation of two popular evidence-accumulation models: the diffusion decision model (DDM) and the linear ballistic accumulator (LBA). It enables individual and hierarchical estimation, as well as assessment of the quality of a model's parameter estimates and descriptive accuracy. First, we introduce the basic concepts of Bayesian parameter estimation, guiding the reader through a simple DDM analysis. We then illustrate the challenges of fitting evidence-accumulation models using a set of LBA analyses. We emphasize best practices in modeling and discuss the importance of parameter- and model-recovery simulations, exploring the strengths and weaknesses of models in different experimental designs and parameter regions. We also demonstrate how DMC can be used to model complex cognitive processes, using as an example a race model of the stop-signal paradigm, which is used to measure inhibitory ability. We illustrate the flexibility of DMC by extending this model to account for mixtures of cognitive processes resulting from attention failures. We then guide the reader through the practical details of a Bayesian hierarchical analysis, from specifying priors to obtaining posterior distributions that encapsulate what has been learned from the data. Finally, we illustrate how the Bayesian approach leads to a quantitatively cumulative science, showing how to use posterior distributions to specify priors that can be used to inform the analysis of future experiments.
Critical evaluation of current data analysis strategies for psychophysiological measures of fear conditioning and extinction in humans.
Scientific advances across a range of disciplines hinge on the ability to make inferences about unobservable theoretical entities on the basis of empirical data patterns. Accurate inferences rely on both discovering valid, replicable data patterns and accurately interpreting those patterns in terms of their implications for theoretical constructs. The replication crisis in science has led to widespread efforts to improve the reliability of research findings, but comparatively little attention has been devoted to the validity of inferences based on those findings. Using an example from cognitive psychology, we demonstrate a blinded-inference paradigm for assessing the quality of theoretical inferences from data. Our results reveal substantial variability in experts’ judgments on the very same data, hinting at a possible inference crisis.
Many models of response time that base choices on the first evidence accumulator to win a race to threshold rely on statistical independence between accumulators to achieve mathematical tractability (e.g.,
Base-rate neglect is a failure to sufficiently bias decisions toward a priori more likely options. Given cognitive and neurocognitive model-based evidence indicating that, in speeded choice tasks, (1) age-related slowing is associated with higher and less flexible overall evidence thresholds (response caution) and (2) gains in speed and accuracy in relation to base-rate bias require flexible control of choice-specific evidence thresholds (response bias), it was hypothesised that base-rate neglect might increase with age due to compromised flexibility of response bias. We administered a computer-based perceptual discrimination task to 20 healthy older (63-78 years) and 20 younger (18-28 years) adults where base-rate direction was either variable or constant over trials and so required more or less flexible bias control. Using an evidence accumulation model of response times and accuracy (specifically, the Linear Ballistic Accumulator model; Brown & Heathcote, 2008), age-related slowing was attributable to higher response caution, and gains in speed and accuracy per base-rate bias were attributable to response bias. Both age groups were less biased than required to achieve optimal accuracy, and more so when base-rate direction changed frequently. However, bias was closer to optimal among older than younger participants, especially when base-rate direction was constant. We conclude that older participants performed better than younger participants because of their greater emphasis on accuracy, and that, by making greater absolute and equivalent relative adjustments of evidence thresholds in relation to base-rate bias, flexibility of bias control is at most only slightly compromised with age.
Deciding not to choose 1We propose a dynamic theory of decisions not to choose which of two options is correct. Such "don't-know" judgements are of theoretical and practical importance in domains ranging from comparative psychology, psychophysics, episodic memory and metacognition to applied areas including educational testing and eyewitness testimony. However, no previous theory has provided a detailed quantitative account of the time it takes to make both definitive and don'tknow responses and their relative frequencies. We tested our theory, the "Multiple Threshold Race" (MTR), in one recognition memory experiment where participants had to pick a previously studied target out of two similar faces and another where targets and lures were tested one at a time. In both experiments we manipulated similarity through face morphing. High similarity made decisions difficult, encouraging don't-know responses. We also tested the MTR's ability to account for other manipulations that aimed to affect the speed and probability of don'tknow responses, including increasing penalties for making an error (with no penalty for a don'tknow response) and emphasising either response speed or accuracy. We found that there were marked individual differences in don't-know use, and that the MTR was able to account for the intricate pattern of effects associated with our manipulations, both on average and in terms of individual differences. We discuss how estimates of MTR's parameters illuminate the psychological mechanisms that govern the interplay between definitive and don't-know responding.
We propose a dynamic theory of decisions not to choose between two options. Such “don’t-know” judgements are of theoretical and practical importance in domains ranging from comparative psychology, psychophysics, episodic memory and metacognition to applied areas including educational testing and eyewitness testimony. However, no previous theory has provided a general account of both the time it takes to make both definitive and don't-know responses and their relative frequencies. We tested our theory, the “Multiple Threshold Race” (MTR), in one recognition memory experiments where participants had to pick a previously studied target out of two similar faces and another where targets and lures were tested one at a time. High similarity made decisions difficult, encouraging don't-know responses, and we manipulated similarity through face morphing. We also tested the MTR’s ability to account for other manipulations that aimed to affect the speed and probability of don't-know responses, including increasing penalties for making an error (with no penalty for a don't-know response) and emphasising either response speed or accuracy. We found that there were marked individual differences in don't-know use, and that the MTR was able to provide a detailed account of the intricate pattern of effects associated with our manipulations, both on average and in terms of individual differences. We discuss how estimates of MTR’s parameters illuminate the psychological mechanisms that govern the interplay between definitive and don't-know responding.
We propose a new approach to cognitive aging research, in which detailed cognitive modelling of a single complex task affords simultaneous measures of the major mechanisms proposed to explain age-related deficits: capacity limits, processing speed, inhibition, and executive function. The validity of these measures rests on their well-defined roles of the model parameters and the model’s precise and comprehensive account of the behaviour of our healthy older (63–78 years) and younger (18–28 years) participants. Processing speed was identified as the primary cause of age-related deficits. Executive control was better for older than younger participants when task demands were lower, but as demands increased this advantage reduced or disappeared, suggesting age-related capacity limitations. These results show that detailed process modelling of a complex task provides a powerful, efficient, and conceptually rich way of gaining new insights into the non-linear interactions among psychological mechanisms that underpin cognitive aging.
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