The Annals of Applied Statistics

Nonstationary modelling of tail dependence of two subjects’ concentration

Kshitij Sharma, Valérie Chavez-Demoulin, and Pierre Dillenbourg

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We analyse eye-tracking data to understand how people collaborate. Our dataset consists of time series of measurements for eye movements, such as spatial entropy, calculated for each subject during an experiment when several pairs of participants collaborate to accomplish a task. We observe that pairs with high collaboration quality obtain their highest values of concentration (or equivalently lowest values of spatial entropy) occurring simultaneously. In this paper, we propose a flexible model that describes the tail dependence structure between two subjects’ entropy when the pair is collaborating. More generally, we develop a generalized additive model (GAM) framework for tail dependence coefficients in the presence of covariates. As for any GAM-type model, the methodology can be used to predict collaboration quality or to explore how joint concentration depends on other cognitive operations and varies over time.

Article information

Ann. Appl. Stat., Volume 12, Number 2 (2018), 1293-1311.

Received: August 2016
Revised: October 2017
First available in Project Euclid: 28 July 2018

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Collaborative learning copulas entropy generalized additive models tail dependence


Sharma, Kshitij; Chavez-Demoulin, Valérie; Dillenbourg, Pierre. Nonstationary modelling of tail dependence of two subjects’ concentration. Ann. Appl. Stat. 12 (2018), no. 2, 1293--1311. doi:10.1214/17-AOAS1111.

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