What kind of elliptical construction would the following interpretation fall into and what are some similar examples?

Here is the sentence construction:

As you come to him, a living stone rejected by men but in the sight of
God chosen and precious, you yourselves like living stones are being
built up.

I want to argue that the phrase "rejected by men but in the sight of God chosen and precious" is implied in the second part of the sentence. In other words I want to argue for an elliptical construction like this:

As you come to him, a living stone rejected by men but in the sight of
God chosen and precious, you yourselves like living stones (rejected
by men but in the sight of God chosen and precious) are being built
up.

What kind of elliptical construction would this be and what are some other examples of it? If it is not an elliptical construction, what kind of construction is it?