In social network studies, most often only a single relation (or link) between the actors is investigated. When more than one link has been recorded, the twoway sociomatrix becomes a three-way array with the set of links being the third way. In this paper, we present a model which simultaneously accounts for the three ways in the data. Random effects are used to model the between-actor variability, both on senders and receivers side. In addition, structural relations between the linking variables are investigated. The model is applied to a study of popularity and strength in a class of students. It is shown that popularity can be seen as a linear function of strength on the receivers' side, but not on the senders' side.