Political science professor Hans Hassell of Cornell College in Iowa has posted a paper, “The Non-existent Primary-Ideology Link, or Do Open Primaries Actually Limit Party Influence in Primary Elections?”  He finds that in open primary states in which a major party has a fair chance of winning a seat, the party organization is able to help its preferred nominee, and discourage candidates it doesn’t like, by using its influence over individuals and organizations that make big donations.

The paper only deals with open primary states, not top-two primary states.