In this paper, we propose and analyze a model built to treat data presenting the following characteristics: 1. they appear in an aggregated form 2. the aggregated terms may be considered as multivariate measures performed by instruments of random accuracy, or by the same instrument of random accuracy, or by the same instrument in changing conditions 3. the data have a p-way classification. This type of data is encountered in several situations, including railroad or telephone demand studies or other network analyses. In the context of a regression model, we provide explicit estimators for the covariance matrix of the response, and discuss their characteristics and limitations. The model is applied to a set of real data. The interpretation of the result incidently allows us to illustrate special features of the family on non-Gaussian compound normal distributions