Could implementation of the schema type LocalBusiness have an adverse affect on a site's national rankings? I wondered if search engines take the presence of LocalBusiness markup as a sign to rank the site less favourably in national results? In kind of the same way that you optimise a site for either local OR national generally. Any thoughts on this?
Like Simon Hayter said, you can have local schema on a site that is national and it will not affect your ranking.
Structured data does not directly impact your rankings but has a more indirect affect. If anything, local data may have an impact on your rankings in local search but will not impact national search.
If your rankings do drop since implementing the code, check you are following guidelines and not receiving any penalties.