Apply a model to or for?

Question

In this research, two types of assessment models have been applied for/to the sample.

Do we apply a model to or for something in research?

Or shall I paraphrase it?

In this research, two types of models have been used to assess the sample.

Answer 1

To is probably more idiomatic for this context:

We applied this model to the data, to show that ...

However you can also simply use model as a verb:

In the same way, we have modeled the data to show that ...

For is used when talking about the model's purpose or justification.

Glasgow was once the 'murder capital of Europe.' Now it's a model for cutting crime.

Answer 2

This whole concept is surely the wrong way round. The world, from which the sample has been taken, is how it is, without regard to any models that you might have chosen to use through which to view the world. So models are not applied, but are tested. You are not testing the sample, you are testing your models. So " we tested our model with these data and..."