Mathematical notation for glmer (GLMM)? I'm looking for the mathematical notation equivalent of:
glmer(ret15i~AARC_Ret+(1|METRO)+ret02i)

I have a model; it is neither a HLM nor a GLM, but both. It is referred to (variously) as a hierarchical generalized linear model, a generalized linear mixed model, a multi-level non-linear mixed effect model, etc. Generalized Linear Models require a link function. The hierarchical nature of my data means I'll have both fixed and random effects. I know what distribution I'm using: Poisson. As formulated in R, this suggests my random effects are limited to random intercept.

From: STATA Multilevel Mixed Effects Reference Manual Release 13.
 A: GLMM notation:
This is the best thing I've found so far (on the internet). 


"Generalized linear mixed models are typically constructed by
  incorporating random effects into the linear predictor of a
  conditionally independent exponential family model. I now formalize
  that notion with the following definition of a generalized linear
  mixed model:  In this definition we see the usual ingredients of a
  generalized linear model. First, the distribution of Yi from an
  exponential family (in this case the distribution is assumed to hold
  conditional on the random effects u). Second, a link function, g(-) is
  applied to the conditional mean of Yi given u to obtain the
  conditional linear predictor. Finally, the linear predictor is assumed
  to consist of two components, the fixed effects portion, described by
  x'13 and the random effects portion, z'u, for which a distribution is
  assigned to u"

McCulloch, C. E., & Neuhaus, J. M. (2014). Generalized linear mixed models. Wiley StatsRef: Statistics Reference Online.
