To cite the iop package in publications use:

Bagozzi B (2026). iop: Inflated Ordered Probit and Logit Models. R package version 0.1.0, https://github.com/bagozzib/iop.

The middle-inflated ordered probit is introduced in:

Bagozzi B, Mukherjee B (2012). “A mixture model for middle category inflation in ordered survey responses.” Political Analysis, 20(3), 369–386. doi:10.1093/pan/mps020.

The zero-inflated ordered probit in political science:

Bagozzi B, Hill D, Moore W, Mukherjee B (2015). “Modeling two types of peace: The zero-inflated ordered probit (ZiOP) model in conflict research.” Journal of Conflict Resolution, 59(4), 728–752. doi:10.1177/0022002713520530.

The top-inflated ordered probit:

Bagozzi B, Joo M, Mukherjee B (2024). “Top-category inflation in ordered international relations outcomes.” Foreign Policy Analysis, 20(2), orae006. doi:10.1093/fpa/orae006.

Corresponding BibTeX entries:

  @Manual{,
    title = {iop: Inflated Ordered Probit and Logit Models},
    author = {Benjamin E. Bagozzi},
    year = {2026},
    note = {R package version 0.1.0},
    url = {https://github.com/bagozzib/iop},
  }

  @Article{,
    title = {A mixture model for middle category inflation in ordered
      survey responses},
    author = {Benjamin E. Bagozzi and Bumba Mukherjee},
    journal = {Political Analysis},
    year = {2012},
    volume = {20},
    number = {3},
    pages = {369--386},
    doi = {10.1093/pan/mps020},
  }

  @Article{,
    title = {Modeling two types of peace: The zero-inflated ordered
      probit (ZiOP) model in conflict research},
    author = {Benjamin E. Bagozzi and Daniel W. Hill and Will H. Moore
      and Bumba Mukherjee},
    journal = {Journal of Conflict Resolution},
    year = {2015},
    volume = {59},
    number = {4},
    pages = {728--752},
    doi = {10.1177/0022002713520530},
  }

  @Article{,
    title = {Top-category inflation in ordered international relations
      outcomes},
    author = {Benjamin E. Bagozzi and Minnie M. Joo and Bumba
      Mukherjee},
    journal = {Foreign Policy Analysis},
    year = {2024},
    volume = {20},
    number = {2},
    pages = {orae006},
    doi = {10.1093/fpa/orae006},
  }