Bayes factors for state-trace analysis

Abstract

h i g h l i g h t s• We develop a new across-subjects Bayesian state-trace analysis.• We present an improved computational method for Bayesian state-trace analysis.• We apply our new methods to an existing data set. a b s t r a c tState-trace methods have recently been advocated for exploring the latent dimensionality of psychological processes. These methods rely on assessing the monotonicity of a set of responses embedded within a state-space. proposed Bayes factors for state-trace analysis, allowing the assessment of the evidence for monotonicity within individuals. Under the assumption that the population is homogeneous, these Bayes factors can be combined across participants to produce a ''group'' Bayes factor comparing the monotone hypothesis to the non-monotone hypothesis. However, combining information across individuals without assuming homogeneity is problematic due to the nonparametric nature of state-trace analysis. We introduce group-level Bayes factors that can be used to assess the evidence that the population is homogeneous vs. heterogeneous, and demonstrate their utility using data from a visual change-detection task. Additionally, we describe new computational methods for rapidly computing individual-level Bayes factors. (C.P. Davis-Stober).Bayes factors that we develop to address the question of monotonicity, and hence the dimensionality, of binary dependent variables, are based on the work of Klugkist, Laudy, and Hoijtink (2005) as applied to state-trace analysis by Prince, Brown, and Heathcote (2012). The aim of Prince et al.'s approach is to preserve the essentially non-parametric nature of state-trace analysis by making only fairly minimal statistical assumptions, the main one being that the dependent variable has a binomial distribution.Prince, Hawkins, Love, and Heathcote's (2012) approach primarily focused on separate analyses of each participant's data, as they showed that state-trace analysis could be invalid when applied to data averaged over participants. In particular, they provided examples where the average of two monotonic relationships is non-monotonic. For inference at the group level, they suggested taking the product of individual participant's Bayes factors, but acknowledged the weakness in two necessary underlying assumptions: (1) that participants are either all of one type (e.g., monotonic) or another (e.g., non-monotonic) and (2) that the participants are entirely unrelated. At first sight, hierarchical http://dx.

Fleeting Perceptual Experience and the Possibility of Recalling Without Seeing

“…We calculate our posterior using the library provided in 21 . We follow 21 in referring to this calculation as BF N/NM , the bayes factor comparing the monotonic versus non-monotonic models.…”

“…The ability to differentially affect behaviours on different tasks is seen as evidence that the mental processes underlying them are in some way functionally separate. However, despite their wide use in the literature, it has been argued that while dissociations are certainly indicative, they do not strictly provide either a necessary or sufficient basis for determining the separation of mental processes [19][20][21] . Broadly, it has been proposed that it is possible to construct cases in which dissociations exist but separate mental processes do not [19][20][21] , and to create cases in which there are separate mental processes without dissociations.…”

“…Regardless, even if a double dissociation of the required kind between experience and reportability was widely agreed to exist, there has been a long standing debate about the use of double dissociations as a measure by which to assess functional differentiation [19][20][21] . In this work, we adopt an alternative method to traditional dissociation logic.…”

“…State trace analysis examines the monotonicity of data, across a state-trace plot in which our two task performances form the axes. In this work, we follow Prince, Brown and Heathcote 22 and Davis-Stober et al 21 in advocating the use of a Bayesian approach to the analysis of these problems. The main reason for this is that we are solving a model comparison problem: comparing whether a non-monotonic or monotonic model best fits our data.…”

In Search of the Factors Behind Naive Sentence Judgments: A State Trace Analysis of Grammaticality and Acceptability Ratings

“…In contrast, if there are multiple processes or mental resources underlying task performance, points on the state trace plot are not so constrained, and are overwhelmingly more likely to "break the line" than not. Various frequentist (Kalish et al, 2016) and Bayesian (Prince et al, 2012;Davis-Stober et al, 2016;Cox and Kalish, 2019) formulations for state trace analyses exist, but in essence all report on whether or not it is possible to conclude that the "line has been broken" while allowing for noisy measurement. The implementation used here is the frequentist one due to Kalish et al (2016).…”