Using only spatially and temporally replicated point counts, Royle (2004b, Biometrics 60, 108-115) developed an N-mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown. One assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration, births, and deaths throughout the study. In the past this has been verified solely by biological arguments related to the study design as no statistical verification was available. In this article, we propose a generalization of the N-mixture model that can be used to formally test the closure assumption. Additionally, when applied to an open metapopulation, the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption. A simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original N-mixture model. The proposed model is then applied to two data sets of avian point counts. The first example demonstrates the closure test on a single-season study of Mallards (Anas platyrhynchos), and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of American robins (Turdus migratorius) from a multi-year study.

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We introduce an approximation to the Gaussian copula likelihood of Song, Li, and Yuan (2009, Biometrics 65, 60-68) used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes. Our approximation allows estimation of parameters from response vectors of length much larger than three, and is asymptotically equivalent to the Gaussian copula likelihood. We estimate regression parameters from the toenail infection data of De Backer et al. (1996, British Journal of Dermatology 134, 16-17), which consist of binary response vectors of length seven or less from 294 subjects. Although maximizing the Gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation (GEE) estimators, our simulation study illustrates that for finite samples, GEE estimators can actually be as much as 20% more efficient.

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[1] Oregon's forested coastal watersheds support important cold-water fisheries of salmon and steelhead (Oncorhynchus spp.) as well as forestry-dependent local economies. Riparian timber harvest restrictions in Oregon and elsewhere are designed to protect stream habitat characteristics while enabling upland timber harvest. We present an assessment of riparian leave tree rule effectiveness at protecting streams from temperature increases in the Oregon Coast Range. We evaluated temperature responses to timber harvest at 33 privately owned and state forest sites with Oregon's water quality temperature antidegradation standard, the Protecting Cold Water (PCW) criterion. At each site we evaluated stream temperature patterns before and after harvest upstream, within, and downstream of harvest units. We developed a method for detecting stream temperature change between years that adhered as closely as possible to Oregon's water quality rule language. The procedure provided an exceedance history across sites that allowed us to quantify background and treatment (timber harvest) PCW exceedance rates. For streams adjacent to harvested areas on privately owned lands, preharvest to postharvest year comparisons exhibited a 40% probability of exceedance. Sites managed according to the more stringent state forest riparian standards did not exhibit exceedance rates that differed from preharvest, control, or downstream rates (5%). These results will inform policy discussion regarding the sufficiency of Oregon's forest practices regulation at protecting stream temperature. The analysis process itself may assist other states and countries in developing and evaluating their forest management and water quality antidegradation regulations.

Suppose X(s) and (s) are stationary spatially autocorrelated Gaussian processes and Y(s) = β 0 + β 1 X(s) + (s) for any location s. Our problem is to estimate the β's, particularly β 1 , when X and Y are not necessarily observed in the same location. This situation may arise when the data are recorded by different agencies or when there are missing data values.A natural but naïve approach is to predict ("krige") the missing X's at the locations Y is observed, and then use least squares to estimate ("regress") the β's as if these X's were actually observed. This krige-and-regress estimator is consistent, even when the spatial covariance parameters are estimated. If we use it as a starting value for a Newton-Raphson maximization of the likelihood, the resulting maximum likelihood estimator is asymptotically efficient. We can then use an information-based variance estimator for inference.