I have a reference in which the authors have applied a three-level multilevel model for binary response:
- Prenatal and Delivery Care and Childhood Immunization in Guatemala: Do Family and Community Matter? Demography, Vol. 33, No. 2., pp. 231-247. http://www.jstor.org/stable/2061874
- Teerenstra, S., Lu, B., Preisser, J.S., van Achterberg, T., & Borm, G.F. (2010). Sample size considerations for GEE analyses of three-level cluster randomized trials. Biometrics, 66(4), 1230-1237. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2896994/pdf/nihms-162479.pdf; http://www.bios.unc.edu/~jpreisse/personal/software.htm
- Pituch, K.A., Murphy, D.L., & Tate, R.L. (2010). Three-Level Models for Indirect Effects in School- and Class-Randomized Experiments in Education. The Journal of Experimental Education, 78(1), 60-95.
- Lutz, W., Leon, S.C., Martinovich, Z., Lyons, J.S., & Stiles, W.B. (2007). Therapist effects in outpatient psychotherapy: A three-level growth curve approach. Journal of Counseling Psychology, 54(1), 32-39.
- Tasca, G.A., Illing, V., Joyce, A.S., & Ogrodniczuk, J.S. (2009). Three-level multilevel growth models for nested change data: a guide for group treatment researchers. Psychotherapy Research, 19(4-5), 453-461.
- Ai, X. (2002). Gender differences in growth in mathematics achievement: three-Level longitudinal and multilevel analyses of individual, home, and school influences. Mathematical Thinking and Learning, 4(1), 1–22.
- Segawa, E. (2005). A Growth Model for Multilevel Ordinal Data. Journal of Educational and Behavioral Statistics, 30(4), 369-396.
- Raman, R., & Hedeker, D. (2005). A mixed-effects regression model for three-level ordinal response data. Statistics in Medicine, 24, 3331–3345.http://www.uic.edu/classes/bstt/bstt513/RamanStatMed.pdf
- de Jong, K., Moerbeek, M., & Van der Leeden, R. (2009). A priori power analysis in longitudinal three-level multilevel models: An example with therapist effects. Psychotherapy Research. http://www.informaworld.com/smpp/115353608-31391521/content~db=all~content=a917167003
- Preacher, K. J. (2011). Multilevel SEM strategies for evaluating mediation in three-level data. Multivariate Behavioral Research, 46, 691–731. http://quantpsy.org/pubs/preacher_2011.pdf
- http://quantpsy.org/pubs/preacher.2011.online.appendix.051211.pdf