Abstract: Using the covariance structure induced by the exchangeability of sampling units, a unified approach to the analysis of dyadic data is proposed. Dyadic data, encountered in diallel designs in genetics and other substantive scientific fields, arise when pairs of sampling units are studied. The problem has been addressed independently in a number of different areas of study. This paper argues that dyadic data structures involve the same statistical elements as those of ordinary analysis of variance and multivariate analysis. In addition to a synthesis of the available literature, the article provides a closed form expression of the Gaussian likelihood, the sufficient statistics and their joint distributions, and outlines for EM and ECM algorithms for handling missing data and other complications. The approach is illustrated with an applied example. The objective is to show that the analysis of dyadic data can be developed as a standard statistical method not unlike the analysis of variance, albeit with a multivariate twist. Dyadic data structures can be treated similarly to ordinary factorial structures and have the potential to be more widely used.
Key words and phrases: Analysis of variance, Bayesian inference, Bio model, Cockerham-Weir Model, diallel design, EM algorithm, ECM algorithm, exchangeability, maximum likelihood, Social Relations Model.