Talking about equivalent circuits, we probably should add equivalent in what regard. In a first order, an antenna's equivalent circuit would be expected to approximate it's impedance with a certain accuracy. It won't allow relating lumped circuit elements to individual. antenna elements, because it hasn't to do with the 3D electromagnetical behaviour of the antenna strcuture. Expecting a relation respectively information about radiation patterns and similar properties of the real 3D device misses the nature of the electromagnetic phenomena, I fear.