A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.

Twin studies have been a valuable source of information about the genetic basis of complex traits. To maximize the potential of twin studies, large, worldwide registers of data on twins and their relatives have been established. Here, we provide an overview of the current resources for twin research. These can be used to obtain insights into the genetic epidemiology of complex traits and diseases, to study the interaction of genotype with sex, age and lifestyle factors, and to study the causes of co-morbidity between traits and diseases. Because of their design, these registers offer unique opportunities for selected sampling for quantitative trait loci linkage and association studies. ASCERTAINMENT BIAS A systematic distortion in measuring the true frequency of a phenomenon, such as a trait or a disease, owing to the way in which the data are obtained.