The value of multiple informant methodology for improving the validity in determining organizational properties has been increasingly recognized. However, the majority of empirical research still relies on single (key) informants. This is partly due to the lack of comprehensive methodological narratives and precise recommendations on the application of this important methodology. Therefore, the authors have developed a critical review and derived clear recommendations for the key challenges that researchers face in using multiple informants: (1) Which and how many informants should be considered? (2) How should the consensus among the informants be judged? (3) How are multiple responses combined into a single, organizational response to conduct further data analyses?

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We suggest locally parametric methods for estimating curves, such as boundaries of density supports or fault lines in response surfaces, in a variety of spatial problems. The methods are based on spatial approximations to the local likelihood that the curve passes through a given point in the plane, as a function of that point. The local likelihood might be a regular likelihood computed locally, with kernel weights (e.g. in the case of support boundary estimation) or a local version of a likelihood ratio statistic (e.g. in fault line estimation). In either case, the local likelihood surface represents a function which is relatively large near the target curve, and relatively small elsewhere. Therefore, the curve may be estimated as a ridge line of the surface; we require only a numerical algorithm for tracking the projection of a ridge into the plane. This approach offers several potential advantages over alternative methods. First, the local (log-)likelihood surface can be graphed, and the degree of`ridginess' assessed visually, to determine how the level of local smoothing should be varied in different spatial locations in order to emphasize the ridge and hence the curve adequately. Secondly, the local likelihood surface does not need to be computed in anything like its entirety; once we have a reasonable approximation to a point on the curve we may track it by numerically`walking along' the ridge line. Thirdly, the method is appropriate without change for many different types of spatial explanatory variables Ð gridded, stochastic or otherwise. Three examples are explored in detail; fault lines in response surfaces and in intensity or density surfaces, and boundaries of supports of probability densities.

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A random spatial coverage process whose generating point process is homogeneous Poisson, and whose attached random sets are independent and identically distributed, is called a Boolean model. Motivated by Błaszczyszyn et al. [1], distributional and higher moment properties of the size of clumps (connected clusters of overlapping sets) in this model are derived. This provides some complements to the result on the finiteness of the first moment presented in Hall [3]. The key idea is to construct a certain coupling process for a multitype branching process that dominates the clump size.