Uniform sampling of binary matrices with fixed margins is known as a difficult problem. Two classes of algorithms to sample from a distribution not too different from the uniform are studied in the literature: importance sampling and Markov chain Monte Carlo (MCMC). Existing MCMC algorithms converge slowly, require a long burn-in period and yield highly dependent samples. Chen et al. developed an importance sampling algorithm that is highly efficient for relatively small tables. For larger but still moderate sized tables (300×30) Chen et al.’s algorithm is less efficient. This article develops a new MCMC algorithm that converges much faster than the existing ones and that is more efficient than Chen’s algorithm for large problems. Its stationary distribution is uniform. The algorithm is extended to the case of square matrices with fixed diagonal for applications in social network theory.

Often problems result in the collection of coupled data, which consist of different N-way N-mode data blocks that have one or more modes in common. To reveal the structure underlying such data, an integrated modeling strategy, with a single set of parameters for the common mode(s), that is estimated based on the information in all data blocks, may be most appropriate. Such a strategy implies a global model, consisting of different N-way N-mode submodels, and a global loss function that is a (weighted) sum of the partial loss functions associated with the different submodels. In this paper, such a global model for an integrated analysis of a three-way three-mode binary data array and a two-way two-mode binary data matrix that have one mode in common is presented. A simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study. An application of the model to real psychological data is discussed.

Multiple-set canonical correlation analysis (Generalized CANO or GCANO for short) is an important technique because it subsumes a number of interesting multivariate data analysis techniques as special cases. More recently, it has also been recognized as an important technique for integrating information from multiple sources. In this paper, we present a simple regularization technique for GCANO and demonstrate its usefulness. Regularization is deemed important as a way of supplementing insufficient data by prior knowledge, and/or of incorporating certain desirable properties in the estimates of parameters in the model. Implications of regularized GCANO for multiple correspondence analysis are also discussed. Examples are given to illustrate the use of the proposed technique.

We discuss properties that association coefficients may have in general, e.g., zero value under statistical independence, and we examine coefficients for 2×2 tables with respect to these properties. Furthermore, we study a family of coefficients that are linear transformations of the observed proportion of agreement given the marginal probabilities. This family includes the phi coefficient and Cohen’s kappa. The main result is that the linear transformations that set the value under independence at zero and the maximum value at unity, transform all coefficients in this family into the same underlying coefficient. This coefficient happens to be Loevinger’s H.