Bivariate Binary Data with Missing Values: Analysis of a Field Experiment to Investigate Chemical Attractants of Wild Dogs

Abstract

This article considers design of a field experiment to investigate the effectiveness of various chemical lures or attractants for dingoes, Canis lupus dingo, Australia's native wild dog, and the subsequent analysis of the resulting data. Chemicals were located 50 meters (m) apart at each of 135 sites equally spaced at 500m apart along an approximate straight path about 70 kilometers (km) long, a so-called transect design. Successful attraction to the chemicals was noted each day for seven days. Analysis of the resulting bivariate binary data (successful or not) are carried out to obtain estimates of the effectiveness of the chemicals. Where there was no response at a site this could either have been due to failure of the chemical to attract a dingo, which was present, or absence of the dingo from the site. In order to analyze the resulting data, a model conditioning on dingo presence/absence and hypothesizing a distribution for dingo presence/absence is introduced and estimates of the attractiveness of chemicals (defined as a probability) are obtained using an EM algorithm. Standard errors of estimates are obtained using both asymptotic approximations and a bootstrap for dependent data. An analysis that conditions on observing at least one chemical at a site being visited by a dingo is investigated and estimates obtained. An investigation is made of the information lost by the conditional analysis. Both empirical and theoretical results infer precision is gained by considering the unconditional analyses.