Speed-Accuracy Tradeoff Modeling and its Interface with Experimental Syntax

Abstract

In this chapter, we review key insights gained by using the speed-accuracy tradeoff (SAT) technique to address psycholinguistic and linguistic issues. SAT evidence has been instrumental in integrating sophisticated memory models into psycholinguistic theory, and bears on several linguistic issues in experimental syntax. We explain how SAT can provide clear evidence about time course of processing that is unconfounded by accuracy or probability of interpretation over trials, and in so doing, can fruitfully inform debates about processing and representation.

Statistical Power in Response Signal Paradigm Experiments

“…Otherwise, we selected the simpler model 1δ − 1β − 1λ. Because (Foraker et al, 2018) suggest the use of the adjusted R 2 metric to supplement hypothesis tests, we also tested a more conservative method, in which the more complex model was only selected if its average adjusted R 2 across participants was higher than that of the simpler model, in addition to the relevant parameter difference being significantly different from 0.…”

“…In it, λ (asymptotic accuracy) determines the highest attainable level of accuracy given unlimited processing time, and δ (intercept) and β (rate) jointly determine the processing speed: δ determines at which point the accuracy rises above chance, while β determines how quickly the SATF increases. The reciprocal of the rate β −1 can be interpreted as the time required for the function to reach approximately 63% of the asymptote (e.g., Liu & Smith, 2009;Foraker et al, 2018).…”

“…Analysis of data from response signal paradigm experiments follows a variant of a stepwise model selection procedure sometimes referred to as a hierarchical model testing scheme (e.g., Foraker et al, 2018): The aim is to select the most parsimonious of a range of models of varying complexity according to several criteria. For two-condition experiments, there are 8 candidate models.…”

“…The parameters for each such model are typically estimated separately for each participant by means of numerical optimization minimizing the root mean squared error (RMSD) of the model fit. (Foraker et al, 2018) recommend forward model selection starting with the asymptote parameter λ. As illustrated in Figure 2A, this process works by successively comparing nested models, beginning with the simplest model 1δ − 1β − 1λ and 1δ − 1β − 2λ in order to determine whether to assume one or two asymptotes.…”

“…This finding, as well as a number of other results in the SAT literature (e.g., McElree, Foraker, & Dyer, 2003;Foraker & McElree, 2007;Martin & McElree, 2008;Van Dyke & McElree, 2011) rest on the absence of a significant difference in speed-related parameters of the speed-accuracy tradeoff function. Because SAT data is typically analyzed using a variant of a stepwise model selection procedure known as hierarchical model selection (e.g., Foraker, Cunnings, & Martin, 2018), it is unfortunately not clear how much statistical power such experiments have in order to find differences in processing speed. In order to understand how to interpret such statistical null-results, we conducted a simulation study to determine the amount of statistical power in typical SAT experiments.…”