John R. Sauer
William A. Link
2014
<p>We consider “participation histories,” binary sequences consisting of alternating finite sequences of 1s and 0s, ending with an infinite sequence of 0s. Our work is motivated by a study of observer tenure in the North American Breeding Bird Survey (BBS). In our analysis, <i>j</i> indexes an observer’s years of service and <i>X<span><sub>j</sub> </span></i>is an indicator of participation in the survey; 0s interspersed among 1s correspond to years when observers did not participate, but subsequently returned to service. Of interest is the observer’s duration <i>D</i> = max {<i>j</i>: <i>X<sub><span>j</span></sub></i> = 1}. Because observed records <span><i>X</i> = (<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>,..., <i>X</i><sub>n</sub>)<sup>1</sup> are of finite length, all that we can directly infer about duration is that </span><i>D</i><span> ⩾ max {</span><i>j</i><span> ⩽</span><i>n</i><span>: </span><i>X<sub><span>j</span></sub></i><span> = 1}; model-based analysis is required for inference about </span><i>D</i><span>. We propose models in which lengths of 0s and 1s sequences have distributions determined by the index </span><i>j</i><span> at which they begin; 0s sequences are infinite with positive probability, an estimable parameter. We found that BBS observers’ lengths of service vary greatly, with 25.3% participating for only a single year, 49.5% serving for 4 or fewer years, and an average duration of 8.7 years, producing an average of 7.7 counts.</span></p>
application/pdf
10.1080/03610926.2014.957854
en
Taylor & Francis
Modeling participation duration, with application to the North American Breeding Bird Survey
article