WARNING: Material on this page is not easy to understand.
There are seven sources of variance in triadic ratings:
judge: a judge's general view of how people see others
perceiver: how people think a person tends to see others
target: how people think a person is seen by others
judge by perceiver: disagreements between judges in how a person sees others
judge by target: disagreements between judges in how a person is seen by others
perceiver by target: agreement between judges in how a person uniquely views a target
judge by perceiver by target: most of this is likely error
There are 16 univariate correlations:
The are so many bivariate correlations that they are too numerous to describe. In general, each a variable can be correlated with all other components at that level. So individual effects are correlated with individual effects, dyadic with dyadic, and triadic with triadic.
Most of the work that I have done on triadic analyses of perception has been with Charles Bond. Many of the insights and almost all of the math are due to him.
Bond, C. F., Jr., Horn, E. M., & Kenny, D. A. (1997). A model for triadic relations. Psychological Methods, 2, 79-94. doi:10.1037/1082-989X.2.1.79
Kenny, D. A., Bond, C. F., Jr., Mohr, C. D., & Horn, E. M.(1996). Do we know how much people like one another? Journal of Personality and Social Psychology, 71, 928-936. doi:10.1037/0022-35184.108.40.2068