Signal detection theory and vestibular perception: II. Fitting perceptual thresholds as a function of frequency

Abstract

Vestibular perceptual thresholds are defined by a dynamic sensory system. To capture these dynamics, thresholds were previously fit as a function of frequency. In this paper, we compare fits using two published models with two new models. Furthermore, a new fitting method that utilizes vestibular perceptual dynamics is developed to improve fit quality and overcome problems associated with the conventional approach. Combinations of the four models and two fitting methods are tested using both simulated data and previously published experimental data. Simulations reveal that the conventional approach underestimates thresholds when the number of trials at each frequency is limited (circa 50); this underestimation is reduced fivefold by the new fitting method that simultaneously utilizes data across frequencies. The new fitting method also scored best for goodness of fit for both the simulations and experimental data. In fact, the new approach of fitting simultaneously across frequencies proved more accurate, more precise, more robust, and more efficient than the conventional approach of fitting the responses at each frequency individually and then fitting these threshold data across frequency. The revised fit of published yaw rotation threshold data show that these are best fit by a first-order high-pass filter having a plateau of 0.5°/s (roughly a factor of 4 higher than the motion platform vibration) at frequencies above the cut-off frequency of 0.26 Hz, which is well above the cut-off frequency of the semicircular canals (circa 0.03 Hz). This dynamic analysis suggests the contributions of a velocity leakage mechanism to human yaw rotation thresholds.

Determining thresholds using adaptive procedures and psychometric fits: evaluating efficiency using theory, simulations, and human experiments

“…Figure 1A shows an example of a psychometric function with μ = 0.5 and σ = 1. This notation is consistent with our earlier papers (Merfeld 2011;Lim and Merfeld 2012;Chaudhuri and Merfeld 2013). …”

“…Although collecting additional responses can improve precision (Taylor and Creelman 1967;Taylor 1971), this takes additional time. Thoughtful selection of stimuli can improve precision without additional responses, which saves time and thus improves efficiency (Wetherill 1963;Kaernbach 1991;Treutwein 1995;Pentland 1980;Harvey 1986;Hall 1968;Hall 1981;Watt and Andrews 1981;Green 1990;Garcia-Perez 1998;Leek 2001;Merfeld 2011;Lim and Merfeld 2012). Indeed, it seems possible to get “something for nothing;” for example, large stimuli to which subjects will consistently respond correctly provide little useful information about threshold, as do tiny stimuli for which subjects are guessing.…”

Signal detection theory and vestibular perception: III. Estimating unbiased fit parameters for psychometric functions

“…The psychometric function assumptions and notation used in this paper are the same as those used in earlier papers in this series (Merfeld 2011; Lim and Merfeld 2012). Specifically, the psychometric function is assumed to be a cumulative Gaussian distribution.…”

“…Furthermore, GLM fits are often used to fit psychometric functions (e.g. Knoblauch and Maloney 2008; Lim and Merfeld 2012, Yssaad-Fesselier & Knoblauch 2006; Zupan and Merfeld 2008), and are a natural choice for our vestibular application where subject responses are binary (e.g., Did I move left or right?) and the psychometric function ranges from 0% to 100%.…”

“…In earlier papers in this series, we presented how signal detection theory relates to the measurement of vestibular thresholds (Merfeld 2011) and presented an investigation of fitting vestibular threshold data across frequencies (Lim and Merfeld 2012). While we remain focused on vestibular applications, this paper focuses on a more general problem – how to perform psychometric function fits that yield less biased parameter estimates for adaptive sampling procedure data than existing approaches (e.g., Wichmann and Hill 2001a; Treutwein and Strasburger 1999).…”