This paper proposes an image segmentation method for synthetic aperture radar (SAR), exploring statistical properties of SAR data to characterize image regions. We consider G⁰A distribution parameters for SAR image segmentation, combined to the level set framework. The G⁰A distribution belongs to a class of G distributions that have been successfully used to model different regions in amplitude SAR images for data modeling purpose. Such statistical data model is fundamental to deriving the energy functional to perform region mapping, which is input into our level set propagation numerical scheme that splits SAR images into homogeneous, heterogeneous, and extremely heterogeneous regions. Moreover, we introduce an assessment procedure based on stochastic distance and the G⁰A model to quantify the robustness and accuracy of our approach. Our results demonstrate the accuracy of the algorithms regarding experiments on synthetic and real SAR data.

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We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.

Summary We review some results on the analysis of longitudinal data or, more generally, of repeated measures via linear mixed models starting with some exploratory statistical tools that may be employed to specify a tentative model. We follow with a summary of inferential procedures under a Gaussian set‐up and then discuss different diagnostic methods focusing on residual analysis but also addressing global and local influence. Based on the interpretation of diagnostic plots related to three types of residuals (marginal, conditional and predicted random effects) as well as on other tools, we proceed to identify remedial measures for possible violations of the proposed model assumptions, ranging from fine‐tuning of the model to the use of elliptically symmetric or skew‐elliptical linear mixed models as well as of robust estimation methods. We specify many results available in the literature in a unified notation and highlight those with greater practical appeal. In each case, we discuss the availability of model diagnostics as well as of software and give general guidelines for model selection. We conclude with analyses of three practical examples and suggest further directions for research.

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Residuals are frequently used to evaluate the validity of the assumptions of statistical models and may also be employed as tools for model selection. For standard (normal) linear models, for example, residuals are used to verify homoscedasticity, linearity of effects, presence of outliers, normality and independence of the errors. Similar uses may be envisaged for three types of residuals that emerge from the fitting of linear mixed models. We review some of the residual analysis techniques that have been used in this context and propose a standardization of the conditional residual useful to identify outlying observations and clusters. We illustrate the procedures with a practical example.

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