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Quantile regression estimates of animal response to spatially structured resources.
ABSTRACT- Estimates of animal responses to their physical environment in spatially structured landscapes commonly have hidden biases because all factors limiting the organism are not measured and accounted for in statistical models. One possible approach to help account for effects of important unmeasured factors is to include a spatial component in the model, based on the assumption that unmeasured factors are spatially structured. A simple way to implement spatial structuring in a regression model is by including a spatial trend surface as some low order polynomial function of latitudinal and longitudinal coordinates of sample locations. Simulations with quantile regression demonstrate that less biased estimates of effects of environmental predictors and more variation in animal response were explained by models that included terms for the spatial trend. Considerable heterogeneity in responses remain unless the unmeasured factors are strongly correlated ( R > 0.9) with spatial trend and, thus, quantile regression is useful for providing estimates of differing rates of change across the probability distribution. When there are heterogeneous responses in a regression model there is no longer a single rate of change that characterizes how the probability distribution is affected by covariates. Some subset of quantiles [0, 1], typically upper quantiles near the maximum when interference interactions between measured and unmeasured factors predominate, provides less biased estimates. Quantile regression with a spatial trend surface and physical environmental covariates is used for estimating bivalve mussel (Macomona liliana) response to spatially structured tidal processes in a New Zealand harbor, data previously analyzed with least squares regression (Legendre et al. 1997).
Key words: regression, limiting factors, quantiles, habitat