Statistica Sinica 17(2007), 735-748

TESTING DYNAMIC RULES OF ANIMAL COGNITIVE

PROCESSING WITH LONGITUDINAL

DISTRIBUTION DATA

Fushing Hsieh$^{1,3}$, Shwu-Bin Horng$^2$, Hui-Ying Lin$^3$ and Yen-Chiu Lan$^3$

$^1$University of California at Davis, $^2$National Taiwan University

and $^3$Academia Sinica

Abstract: Identifying the cognitive capacity used by an animal to resolve its foraging task when facing ever-changing environmental conditions is a recent, central issue in behavioral ecology and cognitive science. Statistical confirmation of potential capacity through analysis of individual behavioral processes becomes an important research topic. New longitudinal data arisec as a sequence of global quality distributions, representing sparsely observed environmental dynamics. Such dynamics result from an individual animal's decision-making process as it explores a patch that consists of a fixed amount of hosts. Three dynamic rules having distinct degrees of cognitive capacities are analyzed under a time-varying Markov structure. From the perspective of goodness-of-fit, two tests statistics are proposed for capturing different aspects of dynamic changes in the environmental. It is found that the test that best embraces the concept of distribution via the receiver operating characteristic (ROC) curve performs quite well.

Key words and phrases: Egg-distribution data, goodness-of-fit test, martingale central limit theory, maximum likelihood approach, receiver operating characteristic (ROC) curve.