Nonparametric testing of the existence of modes

Minnotte, Michael C.

doi:10.1214/aos/1031594735

Cited by 75 publications

(53 citation statements)

References 17 publications

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“…First, we have focused here on bimodality estimations in an "out-of-the-box" style by using readily available methods. Researchers interested in detailed density estimation techniques may go beyond bimodality and into the domain of fitting complex mixture models (for some exploration of the mathematical properties of these measures, see Hartigan & Hartigan, 1985;Minnotte, 1997;Silverman, 1981; and in other scientific domains, Hellwig et al, 2010;Milligan & Cooper, 1985). We hope that the estimations described here are helpful for researchers and are able to be used as generalpurpose techniques to distinguish unimodal and bimodal distributions in commonly observed experimental data.…”

Section: Limitationsmentioning

confidence: 95%

Assessing bimodality to detect the presence of a dual cognitive process

2012

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Researchers have long sought to distinguish between single-process and dual-process cognitive phenomena, using responses such as reaction times and, more recently, hand movements. Analysis of a response distribution's modality has been crucial in detecting the presence of dual processes, because they tend to introduce bimodal features. Rarely, however, have bimodality measures been systematically evaluated. We carried out tests of readily available bimodality measures that any researcher may easily employ: the bimodality coefficient (BC), Hartigan's dip statistic (HDS), and the difference in Akaike's information criterion between one-component and two-component distribution models (AIC diff ). We simulated distributions containing two response populations and examined the influences of (1) the distances between populations, (2) proportions of responses, (3) the amount of positive skew present, and (4) sample size. Distance always had a stronger effect than did proportion, and the effects of proportion greatly differed across the measures. Skew biased the measures by increasing bimodality detection, in some cases leading to anomalous interactive effects. BC and HDS were generally convergent, but a number of important discrepancies were found. AIC diff was extremely sensitive to bimodality and identified nearly all distributions as bimodal. However, all measures served to detect the presence of bimodality in comparison to unimodal simulations. We provide a validation with experimental data, discuss methodological and theoretical implications, and make recommendations regarding the choice of analysis.

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Section: Limitationsmentioning

confidence: 95%

Assessing bimodality to detect the presence of a dual cognitive process

2012

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“…Statistically significant peaks were identified in each individual histogram with a mode existence test (Minnotte 1997;Minnotte and Scott 1993). This test provides a multimodal distribution analysis.…”

Section: Methodsmentioning

confidence: 99%

“…Briefly, this test revealed whether each identified peak was either an artifact of the sample or a true feature of the population. Due to the conservative nature of tests for multimodality, peaks were considered significant at P Յ 0.15 (Izenman and Sommer 1988;Minnotte 1997). The output of the mode existence test provided the direction and bounds of each statistically significant peak.…”

Section: Methodsmentioning

confidence: 99%

A preferred pattern of joint coordination during arm movements with redundant degrees of freedom

Dounskaia

Wang

2014

Journal of Neurophysiology

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“…Thus multimodal procedures often entail some subjective aspects. In an attempt to minimize this subjectivity, the mode existence test was recruited to both ascertain whether stroke orientations were uniformly distributed and to study the significance of any suspected directional biases (Minnotte 1997;Minnotte and Scott 1993). This test revealed whether a peak (suspected mode) identified in the polar histogram of orientation data at direction x was either an artifact of the sample or a true feature of the population.…”

Section: Identification Of Significant Peaks and Stroke Clustersmentioning

confidence: 99%

Directional Biases Reveal Utilization of Arm's Biomechanical Properties for Optimization of Motor Behavior

Goble¹,

Zhang²,

Shimansky³

et al. 2007

Journal of Neurophysiology

101

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Strategies used by the CNS to optimize arm movements in terms of speed, accuracy, and resistance to fatigue remain largely unknown. A hypothesis is studied that the CNS exploits biomechanical properties of multijoint limbs to increase efficiency of movement control. To test this notion, a novel free-stroke drawing task was used that instructs subjects to make straight strokes in as many different directions as possible in the horizontal plane through rotations of the elbow and shoulder joints. Despite explicit instructions to distribute strokes uniformly, subjects showed biases to move in specific directions. These biases were associated with a tendency to perform movements that included active motion at one joint and largely passive motion at the other joint, revealing a tendency to minimize intervention of muscle torque for regulation of the effect of interaction torque. Other biomechanical factors, such as inertial resistance and kinematic manipulability, were unable to adequately account for these significant biases. Also, minimizations of jerk, muscle torque change, and sum of squared muscle torque were analyzed; however, these cost functions failed to explain the observed directional biases. Collectively, these results suggest that knowledge of biomechanical cost functions regarding interaction torque (IT) regulation is available to the control system. This knowledge may be used to evaluate potential movements and to select movement of "low cost." The preference to reduce active regulation of interaction torque suggests that, in addition to muscle energy, the criterion for movement cost may include neural activity required for movement control. I N T R O D U C T I O NDemands of daily living promote optimization of movement characteristics, such as speed and accuracy, while minimizing effort for movement production. How this optimization is achieved has been a focus of extensive research in the area of optimal control of human movements. Various cost functions have been proposed (Todorov 2004); however, it is difficult to ascertain what is actually being optimized, as well as how this optimization process is organized. We hypothesize that the CNS exploits biomechanical properties of the limbs to increase efficiency of movement control. The study specifically focuses on biomechanical factors that influence performance of multijoint arm movements. Three such factors have been recognized: interaction torque (IT), inertial resistance, and kinematic manipulability. IT results from mechanical influence of arm segments on each other during motion (Hollerbach and Flash 1982). Inertial resistance characterizes muscle effort necessary to produce a given acceleration of the arm endpoint (Hogan 1985). Kinematic manipulability characterizes angular velocity at the joints required to produce a given endpoint velocity (Yoshikawa 1985(Yoshikawa , 1990.To produce goal-directed movements, muscular control must be adjusted to all these factors. Each factor depends on movement direction, thus imposing differential demands for...

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Nonparametric testing of the existence of modes

Cited by 75 publications

References 17 publications

Assessing bimodality to detect the presence of a dual cognitive process

Assessing bimodality to detect the presence of a dual cognitive process

A preferred pattern of joint coordination during arm movements with redundant degrees of freedom

Directional Biases Reveal Utilization of Arm's Biomechanical Properties for Optimization of Motor Behavior

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