This paper extends the two-component approach to modelling count data with extra zeros, considered by Mullahy (1986), Heilbron (1994 and Welsh et al. (1996), to take account of possible serial dependence between repeated observations. Generalized estimating equations are constructed for each component of the model by incorporating correlation matrices into each of the maximum likelihood estimating equations. The proposed method is demonstrated on weekly counts of Noisy Friarbirds (Philemon corniculatus), which were recorded by observers for the Canberra Garden Bird Survey (Hermes, 1981).

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Spatial designs for monitoring stream networks, especially ephemeral systems, are typically non-standard, `sparse' and can be very complex, reflecting the complexity of the ecosystem being monitored, the scale of the population, and the competing multiple monitoring objectives. The main purpose of this paper is to present a review of approaches to spatial design to enable informed decisions to be made about developing practical and optimal spatial designs for future monitoring of streams.Comment: Published in at http://dx.doi.org/10.1214/07-SS032 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org

We explore the possibility of modelling zero-inflated count data using the Neyman type A distribution. We extend three parameterizations of the Neyman type A distribution to allow their parameters to depend on covariates. We develop models which relate counts of Leadbeater’s possum to various habitat variables to illustrate the methodology. Half-normal plots are constructed for each model to explore the quality of the fit. We then formally compare the Neyman type A models using the method of Cox to test non-nested hypotheses. Finally, we compare each of the Neyman type A models with a model from a competing family, the conditional Poisson model.

An environmental index is the combination of multiple sources of information (i.e., indicators of ecological responses) about an environmental system (e.g., a stream) from potentially varying attributes of that system (e.g., instream processes, ecological processes, species richness, riparian vegetation, etc.). Environmental indices are typically developed to provide an overall snapshot of some feature of the environmental system but they are also used to compare similar environmental systems. The construction of an environmental index requires careful consideration of several important aspects of the individual environmental indicators that contribute to it, namely, defining a theoretical framework for supporting indicator selection; data preparation; standardization of the potentially disparate indicators so that they can easily be combined into an index; weighting and aggregation of the individual indicators; and robustness and sensitivity of the decisions made in constructing an environmental index. By considering all five steps, there is a better chance of producing a transparent, objective, and defensible summary of the attribute of the environmental system.