I just created a stanc3 GitHub issue around adding a zero_sum_vector type and have attached the link below. I’d like this feature because I’m getting tired of coding this all by hand, which requires boilerplate parameter and transformed parameter declarations which bloat the code and make it hard t…

[image] betanalpha: … it breaks infinite exchangeability/conditional independence of the model, making it fundamentally different from classic hierarchal models. Thanks for pointing that out. The model becomes an “intrinsic” model like ICAR instead of a full model like CAR. @betanalpha : Wh…

I was curious about how the posterior would differ between enforcing the sum-to-zero constraint and not. So I’m going to do a little simulation, because it’s easier than doing real math. Simple hierarchical model Let’s consider a simple, canonical random-effects model for binary data organized i…

@avehtari and @bgoodri found my bug during the Stan meeting. Here’s the revised hierarchical model that takes the prior for alpha to be centered at mu. This brings the results in line. Here’s the revised hier-ctr.stan. data { int<lower=0> K; int<lower=0> N; array[K, N] int<lower=0, upper=1>…

I wondered about exactly the same thing a while ago. It turns out that with normal prior on the intercept, you can parametrize the model with sum-to-zero constraint, resolve identifiability issues + remove one parameter, but then recover exactly the same inferences as you would have with the origina…

My intuition is that the mu on the non centered program must span a wider range due to the range of values that alpha may take. In the centered program regardless of where the K - 1 alphas end up in the real line they will always be as close or closer together than the K in the non centered. If a bu…

[image] Bob_Carpenter: Now the question I have is why mu has such a wide distribution in the first model compared to the second. Uncertainty for sigma is similar in both models. The answer to this is something you have already written yourself: [image] Bob_Carpenter: With both seeds, the…

I was trying to put this in a multivariate normal specification to see how we can derive the standard errors using matrix algebra. We want a matrix M which when multiplied by a vector gives the vector plus the negative sum of the elements prior. \alpha M = \bigg[\alpha_1 \:\alpha_2 \: \cdots \: \…

[image] Bob_Carpenter: Thanks for pointing that out. The model becomes an “intrinsic” model like ICAR instead of a full model like CAR. Right. [image] Bob_Carpenter: @betanalpha : Which do you consider the “classic hierarchical model”? The model that pins one of the coefficients is quite …

[image] Bob_Carpenter: Is there an example you had in mind? Just the examples that we are already discussing. I have no quarrel with any of the math here, but I think it is useful to be careful about how we communicate this stuff to users. In my experience, most users are essentially follow…

[image] jsocolar: Note that the same problem already exists for simplex vectors, Simplex is different because the prior is almost always a Dirichlet distribution. It’s readily interpretable as simplexes are the distribution’s natural support. With the “normal” distribution on sum-to-zero vec…

New Stan data type: zero_sum_vector

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spinkney Split this topic March 3, 2022, 3:33pm 16

3 posts were split to a new topic: Sum-to-zero with multiple constraints

Topic		Replies	Views
Proper use of sum_to_zero_vector in nested multilevel models Modeling fitting-issues , specification , matrix , cmdstanr , hierarchical-model	17	574	June 2, 2025
Sum to zero constraints and multi-level models - best practise/example code Modeling	14	930	July 16, 2025
Zero sum vector and normal distribution Modeling	20	1278	February 8, 2025
Correlated posterior - Sum to zero constraint for varying intercepts?! Modeling mixed-model	20	5167	December 22, 2021
Test: Soft vs Hard sum-to-zero constrain + choosing the right prior for soft constrain Modeling	45	8889	September 11, 2023

New Stan data type: zero_sum_vector

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