Summary. We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated measures and longitudinal structures, and the third involves a spatio-temporal analysis of rainfall data. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modelled by means of a link function and a linear predictor. The models are fitted using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, spatial and spatio-temporal structures.

Aedes aegypti has developed evolution-driven adaptations for surviving in the domestic human habitat. Several trap models have been designed considering these strategies and tested for monitoring this efficient vector of Dengue. Here, we report a real-scale evaluation of a system for monitoring and controlling mosquito populations based on egg sampling coupled with geographic information systems technology. The SMCP-Aedes, a system based on open technology and open data standards, was set up from March/2008 to October/2011 as a pilot trial in two sites of Pernambuco -Brazil: Ipojuca (10,000 residents) and Santa Cruz (83,000), in a joint effort of health authorities and staff, and a network of scientists providing scientific support. A widespread infestation by Aedes was found in both sites in 2008–2009, with 96.8%–100% trap positivity. Egg densities were markedly higher in SCC than in Ipojuca. A 90% decrease in egg density was recorded in SCC after two years of sustained control pressure imposed by suppression of >7,500,000 eggs and >3,200 adults, plus larval control by adding fishes to cisterns. In Ipojuca, 1.1 million mosquito eggs were suppressed and a 77% reduction in egg density was achieved. This study aimed at assessing the applicability of a system using GIS and spatial statistic analysis tools for quantitative assessment of mosquito populations. It also provided useful information on the requirements for reducing well-established mosquito populations. Results from two cities led us to conclude that the success in markedly reducing an Aedes population required the appropriate choice of control measures for sustained mass elimination guided by a user-friendly mosquito surveillance system. The system was able to support interventional decisions and to assess the program’s success. Additionally, it created a stimulating environment for health staff and residents, which had a positive impact on their commitment to the dengue control program.

We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form µ + φµ p , where µ is the mean, φ and p are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression methodology for a comprehensive family of count models including Hermite, Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian. The estimating function approach allows us to extend the Poisson-Tweedie distributions to deal with underdispersed count data by allowing negative values for the dispersion parameter φ. Furthermore, the Poisson-Tweedie family can automatically adapt to highly skewed count data with excessive zeros, without the need to introduce zero-inflated or hurdle components, by the simple estimation of the power parameter. Thus, the proposed models offer a unified framework to deal with under, equi, overdispersed, zero-inflated and heavy-tailed count data. The computational implementation of the proposed models is fast, relying only on a simple Newton scoring algorithm. Simulation studies showed that the estimating function approach provides unbiased and consistent estimators for both regression and dispersion parameters. We highlight the ability * Generalized linear models (GLMs) (Nelder and Wedderburn;1972) have been the main statistical tool for regression modelling of normal and non-normal data over the past four decades. The success enjoyed by the GLM framework comes from its ability to deal with a wide range of normal and non-normal data. GLMs are fitted by a simple and efficient Newton score algorithm relying only on second-moment assumptions for estimation and inference. Furthermore, the theoretical background for GLMs is well established in the class of dispersion models (Jørgensen; 1987, 1997) as a generalization of the exponential family of distributions. In particular, the Tweedie family of distributions plays an important role in the context of GLMs, since it encompasses many special cases including the normal, Poisson, non-central gamma, gamma and inverse Gaussian.In spite of the flexibility of the Tweedie family, the Poisson distribution is the only choice for the analysis of count data in the context of GLMs. For this reason, in practice there is probably an over-emphasis on the use of the Poisson distribution for count data. A well known limitation of the Poisson distribution is its mean and variance relationship, which implies that the variance equals the mean, referred to as equidispersion. In practice, however, count data can present other features, namely underdispersion (mean > variance) and overdispersion (mean < variance) that is often related to zero-inflation or a heavy tail. These departures can make the Poisson distribution unsuitable, or at lea...

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