Diagrams for hierarchical models – we need your opinion

(This article was originally published at Doing Bayesian Data Analysis, and syndicated at StatsBlogs.)

When trying to understand a hierarchical model, I find it helpful to make a diagram of the dependencies between variables. But I have found the traditional directed acyclic graphs (DAGs) to be incomplete at best and downright confusing at worst. Therefore I created differently styled diagrams for Doing Bayesian Data Analysis (DBDA). I have found them to be very useful for explaining models, inventing models, and programming models. But my idiosyncratic impression might be only that, and I would like your insights about the pros and cons of the two styles of diagrams.

To make the contrast concrete, let's consider the classic "rats" example from BUGS. I will start with a textual explanation of the model (using modified phrasing and variable names), and then provide two diagrams of the model, one in DAG style and one in DBDA style. Here is the text:

The data come from 30 young rats whose weights were measured weekly starting at birth for five weeks, with the goal being to assess how their weights changed as a function of age. The variable y_j|i denotes the weight of the i^th rat measured at days since birth x_j|i. The weights are assumed to be distributed normally around the predicted value ω_j|i (omega):
y_j|i ~ normal( ω_j|i , λ ) The parameter λ (lambda) represents the precision (i.e., 1/variance) of the normal distribution. The predicted weight of the i^th rat is modeled as a linear function of days since birth:
ω_j|i = φ_i + ξ_i x_j|iThe individual intercepts φ_i (phi) and slopes ξ_i (xi) are assumed to come from group-level normal distributions,
φ_i ~ normal( κ , δ )    and    ξ_i ~ normal( ζ , γ ) where κ (kappa) and ζ (zeta) are the means of the group-level distributions. The priors on the group-level means are set as vague normal distributions,
κ ~ normal( M , H )    and    ζ ~ normal( M , H ) where the mean M is approximately central on the scale of the data and the precision H is very small. The precision parameters, λ (lambda), δ (delta), and γ (gamma), are given vague gamma priors,
λ ~ gamma( K , I )    and    δ ~ gamma( K , I )    and    γ ~ gamma( K , I ) where the shape K and rate I parameters are set to very small values.

Below are two different diagrams of the model. The first is a DAG. Because there are a variety of style conventions in the literature for DAGs, I used my own hybrid explained in the caption. But I think it is a good and useful hybrid, one that I would want to use if I used DAGs. Take a look at the DAG:

Squares denote constants, circles denote variables. Solid arrows denote stochastic dependency, heavy dotted arrows denote deterministic dependency. Rounded-corner rectangles denote "plates" for indices.

For DAG users, does the style above capture what you think is needed in a DAG? Does the DAG above help you understand the model? How? Does the DAG confuse you? Why? Would the DAG help you program the model in BUGS / JAGS / Stan? Or not?

Below is a DBDA-style diagram for the model:

Arrows marked by "~" denote stochastic dependency, arrows marked by "=" denote deterministic dependency. Ellipses on arrows denote indices over which the dependency applies.

Does the DBDA-style diagarm above help you understand the model? How? Does the DBDA-style confuse you? Why? Would the DBDA-style help you program the model in BUGS / JAGS / Stan? Or not?

Please provide your answers as comments on this post. Thank you in advance!

Please comment on the article here: Doing Bayesian Data Analysis