“at this stage” Vs. “in this stage”
The choice of preposition here is a subtle one. It’s useful to look at the relevant definitions:
at (1)
- Expressing the time when an event takes place.
- ‘the children go to bed at nine o’clock’
- ‘his death came at a time when the movement was split’
[Oxford Dictionaries]
In this particular context, “at” identifies a specific moment in the process/timeline. Compare this with:
in (1)
- Expressing a period of time during which an event happens or a situation remains the case.
- ‘at one o’clock in the morning’
- ‘Nobody who is associated with the bank in that period can come out with any credit.’
[Oxford Dictionaries]
Thus, “in” is more general and, in the context of your sentence, covers anything that happened during that stage.
To some degree the choice of preposition is also influenced by the broader context. If the discussion is about the stage itself, then the action happens in (during) that stage. If the discussion is focused on the model itself, then you would describe at what point it’s put into operation.
