There are three kinds of metaphysical models of a theological mystery—say, Trinity, Incarnation or Transubstantiation:
realistic model: a metaphysical story that is meant to be a true account of what makes the mysterious doctrine be true
potential model: a metaphysical story that is meant to be an epistemically possible account of what makes the mysterious doctrine be true
analogical model: a story that is meant to be an epistemically possible account of what makes something analogous to the mysterious doctrine be true.
For instance, Aquinas’s accounts of the Trinity, Incarnation and Transubstantiation are realistic models: they are meant to be accounts of what indeed makes the doctrines true. Van Inwagen’s relative identity account of the Trinity or his body-snatching account of the resurrection, on the other hand, are only potential models: van Inwagen does not affirm they are true. And the history of the Church is filled with analogical models.
A crucial test of any of these models is this: Imagine that you believe the story to be true, and see if the traditional things that one says about the mystery (in the case of a realistic or potential model), or analogues of them (in the case of an analogical model), sound like reasonable things to say given what one believes.
For instance, consider a time-travel model of the Incarnation. Alice, currently a successful ultramarathoner and brilliant geologist, will live a long and fruitful life. Near the end of her life, she has lost most of her physical and mental powers, and all her knowledge of geology. She uses a time machine to go back to 2020 when she is in her prime. If we thought this story was true, it would be reasonable to find ourselves saying things like:
Alice is a successful ultramarathoner and barely able to walk
Alice understands continental drift and does not not know what magma is
Alice is young and old
Alice is in the pink of health and dying.
These things would sound like a contradiction, but the time-travel story shows they are not. However, these claims are also analogous to claims that constitute an especially mysterious part of the mystery of the Incarnation (and I suppose a mysterious part of a mystery is itself a mystery): Christ suffers and is impassible; Christ is omniscient and does not know everything; Christ is timeless and born around 4 BC.
Of course nobody should think that it’s literally true that the Incarnation is to be accounted for in terms of time travel. But what the analogical model does show is that there are contexts in which it is reasonable to describe a non-contradictory reality in terms that are very similar to the apparently contradictory incarnational claims.