Losing favor after 1828, the earliest method of nominating candidates for office was the legislative
caucus
convention
primary
petition

The answer is caucus.  It is a gathering of party members where they organize the actions, policies of the party or select candidates for several offices in government.  They meet to deliberate on choosing a nominee for the Presidency.  It has become an important process in nominating a presidential candidate.

In order to help the student expand his/her knowledge I will help answer the question. This in hope that the student will get a piece of knowledge that will help him/her through his/her homework or future tests.

Losing favor after 1828, the earliest method of nominating candidates for office was the legislative Caucus. This is a meeting of a big organization in this case of the government to select candidates or to decide on new policies.

I hope it helps, Regards.