If you check a model into the repository, you also check in the packages it contains.
While, generally, you need the Write or Full permission to check a document into the repository, you can check in a model on which you only have Read permission if it contains at least one package for which you have Write or Full permission. However, note that any edits made to packages for which you do not have Write or Full permission will be lost during check in.
For information about checking out package, see Checking Out Packages.