Modeling participation duration, with application to the North American Breeding Bird Survey

William A. Link and John R. Sauer

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 21, 6311-6320

Abstract: 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, j indexes an observer’s years of service and Xj 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 D = max {j: Xj = 1}. Because observed records X=(X1,X2,...,Xn)'$\bm X = (X_1, X_2,\ldots ,X_n)^{\prime }$ are of finite length, all that we can directly infer about duration is that D ⩾ max {j ⩽ n: Xj = 1}; model-based analysis is required for inference about D. We propose models in which lengths of 0s and 1s sequences have distributions determined by the index j 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.

Date: 2016
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DOI: 10.1080/03610926.2014.957854

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