Elaborations
When dyad members are distinguishable (e.g., boss and employee) and the analysis uses the logistic or probit function, the researcher is implicitly assuming that there is homogeneity of unexplained variance in the errors or residuals. See Allison (Allison, P. D. (1999). “Comparing logit and probit coefficients across groups. ”Sociological Methods and Research, 28, 186-208.)for more details.
There is a recently published paper on using SAS's PROC NLMIXED with dyads: McMahon, J. M., Pouget, E. R., & Tortu, S. (2006). A guide for multilevel modeling of dyadic data with binary outcomes using SAS PROC NLMIXED.Computational Statistics and Data Analysis, 50, 3663-3680.
SAS can better handle dichotomous and counts using GLIMMIX. See the SAS website for more information. Also there is a paper to be published in Personal Relationships entitled "Extending the actor-partner interdependence model to include binary outcomes: A multilevel logistic approach" by Seth Spain, Joshua J. Jackson and Grant W. Edmonds on this topic.
With binomial and counted data there is overdispersion because the data have
a larger variance than expected under the assumption of a binomial or Poisson distribution. It is possible that there could be under-dispersion. It is advisable to test for over- and under-dispersion because significance tests can be biased. Ignoring over-dispersion leads to tests being too liberal and ignoring under-dispersion leads to test being too liberal. We think that the standard multilevel model in which the dyad effect is model as a variance will likely lead to under-dispersion (but we need to investigate this more). It therefore would seem advisable to adjust for over- or over-dispersion in working with these models. Both HLM and SAS-GLIMMIX can do this.
