To cite package 'cAIC4' itself use the manual and the software paper.

Saefken, B. and Ruegamer, D. (2018), cAIC4: Conditional Akaike information criterion for lme4, R package version 0.3

Saefken, B., Ruegamer, D., Kneib, T., and Greven, S. (2018), Conditional Model Selection in Mixed-Effects Models with cAIC4, ArXiv e-prints 1803.05664.

Corresponding BibTeX entries:

  @Manual{,
    title = {cAIC4: Conditional Akaike information criterion for lme4},
    author = {Benjamin Saefken and David Ruegamer and with
      contributions from Sonja Greven and Thomas Kneib},
    year = {2018},
  }
  @Article{,
    title = {Conditional Model Selection in Mixed-Effects Models with
      cAIC4},
    author = {Benjamin Saefken and David Ruegamer and Thomas Kneib and
      Sonja Greven},
    journal = {ArXiv e-prints},
    year = {2018},
    eprint = {1803.05664},
    month = {march},
  }