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The present study is an analysis of a Czech political corruption network known as the Rath affair reconstructed with publicly available data. We argue that for the study of criminal networks it is fruitful to follow a multiplex approach, i.e., to distinguish several interdependent network dimensions and study how they are interrelated. Relational elements in corruption are identified, and we propose three dimensions that are essential for understanding the Rath network: pre-existing ties (e.g., marriage or co-membership of the same party), resource transfer (e.g., bribing), and collaboration (e.g., communication). The aim of the study was threefold. We aimed to examine if the network exhibits the core/periphery structure, to investigate the multiplex structure of the network by assessing the overlap of the main dimensions of the network, and to determine the central and multiplex actors while considering the differentiation of centrality according to the three network dimensions. The core/periphery model appears to have a perfect fit to the aggregated network, leading to a four-block adjacency matrix. Studying the frequency of ties in these blocks shows that collaboration ties are present in all the blocks, while resource transfer ties are mainly located between the core and periphery, and pre-existing ties are rare generally. We also identify central actors, none of which are strategically positioned, occupying more visible positions instead. The majority of actors display strong multiplexity in the composition of their own ties. In the conclusion the potential usefulness of multiplex descriptive measures and of mixed methods approaches, implications of our results for trust incriminal networks, and potential merits of analytical sociology approach are discussed.

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data.

In this study we try to estimate the size of the homeless population in Budapest by using two – non-standard – sampling methods: snowball sampling and capture-recapture method. Using two methods and three different data sets we are able to compare the methods as well as the results, and we also suggest some further applications. Apart from the practical purpose of our study there is a methodological one as well: to use two relatively unknown methods for the estimations of this very peculiar kind of population.

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.

Three methodological issues are discussed that are important for the analysis of data on networks in organizations. The first is the two-level nature of the data: individuals are nested in organizations. This can be dealt with by using multilevel statistical methods. The second is the complicated nature of statistical methods for network analysis. The third issue is the potential of mathematical modeling for the study of network effects and network evolution in organizations. Two examples are given of mathematical models for gossip in organizations. The first example is a model for cross-sectional data, the second is a model for longitudinal data that reflect the joint development of network structure and individual behavior tendencies.

A statistical approach to a posteriori blockmodeling for graphs is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong. Statistical procedures are derived for estimating the probabilities of edges and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this strategy is practical only for small graphs. A Bayesian estimator, based on Gibbs sampling, is proposed. This estimator is practical also for large graphs. When ML estimators are used, the block structure can be predicted based on predictive likelihood. When Gibbs sampling is used, the block structure can be predicted from posterior predictive probabilities. A side result is that when the number of vertices tends to infinity while the probabilities remain constant, the block structure can be recovered correctly with probability tending to 1. (Less)

Parameters are derived of distributions of three coefficients of similarity between pairs (dyads) of operational taxonomic units for multivariate binary data (presence/absence of attributes) under statistical independence. These are applied to test independence for dyadic data. Association among attributes within operational taxonomic units is allowed. It is also permissible for the two units in the dyad to be drawn from different populations having different presence probabilities of attributes. The variance of the distribution of the similarity coefficients under statistical independence is shown to be relatively large in many empirical situations. This result implies that the practical interpretation of these coefficients requires much care. An application using the Jaccard index is given for the assessment of consensus between psychotherapists and their clients.

The hierarchical linear model in a linear model with nested random coefficients, fruitfully used for multilevel research. A tutorial is presented on the use of this model for the analysis of longitudinal data, i.e., repeated data on the same subjects. An important advantage of this approach is that differences across subjects in the numbers and spacings of measurement occasions do not present a problem, and that changing covariates can easily be handled. The tutorial approaches the longitudinal data as measurements on populations of (subject-specific) functions.

Two test statistics are proposed for testing the equality of two correlated proportions when some observations are missing on both responses. The performance of these tests in terms of size and power is compared with other tests by means of Monte Carlo simulations. The proposed tests are easily computed and compare favorably with other tests.