Statistical modeling is generally meant to describe patterns in data in service of the broader scientific goal of developing theories to explain those patterns. Statistical models support meaningful inferences when models are built so as to align parameters of the model with potential causal mechanisms and how they manifest in data. When statistical models are instead based on assumptions chosen by default, Attempts to draw inferences can be uninformative or even paradoxical—in essence, the tail is trying to wag the dog.These issues are illustrated by van Doorn et al. (in press) in the context of using BayesFactors to identify effects and interactions in linear mixed models. We show that the problems identified in their applications can be circumvented by using priors over inherently meaningful units instead of default priors on standardized scales. This case study illustrates how researchers must directly engage with a number of substantive issues in order to support meaningful inferences, of which we highlight two: The first is the problem of coordination, which requires a researcher to specify how the theoretical constructs postulated by a model are functionally related to observable variables. The second is the problem of generalization, which requires a researcher to consider how a model may represent theoretical constructs shared across similar but non-identical situations, along with the fact that model comparison metrics like Bayes Factors do not directly address this form of generalization. For statistical modeling to serve the goals of science, models cannot be based on default assumptions, but should instead be based on an understanding of their coordination function and on how they represent causal mechanisms that may be expected to generalize to other related scenarios.
Decisions about where to move the eyes depend on neurons in Frontal Eye Field (FEF). Movement neurons in FEF accumulate salience evidence derived from FEF visual neurons to select the location of a saccade target among distractors. How visual neurons achieve this salience representation is unknown. We present a neuro-computational model of target selection called Salience by Competitive and Recurrent Interactions (SCRI), based on the Competitive Interaction model of attentional selection and decision making (Smith & Sewell, 2013). SCRI selects targets by synthesizing localization and identification information to yield a dynamically evolving representation of salience across the visual field. SCRI accounts for neural spiking of individual FEF visual neurons, explaining idiosyncratic differences in neural dynamics with specific parameters. Many visual neurons resolve the competition between search items through feedforward inhibition between signals representing different search items, some also require lateral inhibition, and many act as recurrent gates to modulate the incoming flow of information about stimulus identity. SCRI was tested further by using simulated spiking representations of visual salience as input to the Gated Accumulator Model of FEF movement neurons (Purcell et al., 2010; Purcell, Schall, Logan, & Palmeri, 2012). Predicted saccade response times fit those observed for search arrays of different set size and different target-distractor similarity, and accumulator trajectories replicated movement neuron discharge rates. These findings offer new insights into visual decision making through converging neuro-computational constraints and provide a novel computational account of the diversity of FEF visual neurons.
Evidence accumulation is a computational framework that accounts for behavior as well as the dynamics of individual neurons involved in decision making. Linking these two levels of description reveals a scaling paradox: How do choices and response times (RT) explained by models assuming single accumulators arise from a large ensemble of idiosyncratic accumulator neurons? We created a simulation model that makes decisions by aggregating across ensembles of accumulators, thereby instantiating the essential structure of neural ensembles that make decisions. Across different levels of simulated choice difficulty and speed-accuracy emphasis, choice proportions and RT distributions simulated by the ensembles are invariant to ensemble size and the accumulated evidence at RT is invariant across RT when the accumulators are at least moderately correlated in either baseline evidence or rates of accumulation and when RT is not governed by the most extreme accumulators. To explore the relationship between the low-level ensemble accumulators and high-level cognitive models, we fit simulated ensemble behavior with a standard LBA model. The standard LBA model generally recovered the core accumulator parameters (particularly drift rates and residual time) of individual ensemble accumulators with high accuracy, with variability parameters of the standard LBA modulating as a function of various ensemble parameters. Ensembles of accumulators also provide an alternative conception of speed-accuracy tradeoff without relying on varying thresholds of individual accumulators, instead by adjusting how ensembles of accumulators are aggregated or by how accumulators are correlated within ensembles. These results clarify relationships between neural and computational accounts of decision making.
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