Penalizing parameter to enforce a sum to 0 constraint?

[fweber144]

Do these resources help?:

https://mc-stan.org/docs/stan-users-guide/regression.html#parameterizing-centered-vectors

https://mc-stan.org/docs/stan-users-guide/poststratification.html#multilevel-regression-and-poststratification

Constraining sum of coefficients

I’m building a simple random walk model where y_t \sim N(\beta_1 y_{t-1} + \beta_2 y_{t-2} + \ldots, sigma). I would like to constrain \sum_{k=1}^K \beta_k = 1, but I don’t want to require that each \beta \in (0, 1) so I don’t want to declare this as a simplex. A hack that works for me is to just declare the last \beta as a separate variable (see following code block). Is there a better way to write this? It feels like there should be data { int<lower=1> N; // Number of data int<lower=…

Sum to zero priors with unequally populated categories in MRP

I’m trying to model CCES data (vote outcomes given various demographic variables) using MR (not yet up to the “P” part!) in Stan. Everything works fine–convergence looks good, sampler is fast, parameters make sense, etc.–until I actually introduce the MR bit. One thing I am confused about in particular is the use of sum-to-zero constraints (enforced via a tight prior around 0 on the sum) on the parameter corresponding to a group. I can see why I’d want this, since otherwise I can shift all g…

Correlated posterior - Sum to zero constraint for varying intercepts?!

Hi, so here’s an issue I’ve ran into in a couple analyses where simple uses of varying (random) intercepts resulted in problematic posterior distributions. In particular, the posterior for the overall intercept is negatively correlated with the posterior for all varying intercepts. The problem seems quite fundamental and appears already for simple models, but I have not yet seen it discussed elsewhere. Maybe I am missing something basic? It appears one can get rid of the issue by enforcing a s…

Test: Soft vs Hard sum-to-zero constrain + choosing the right prior for soft constrain

Hello, I have done some tests comparing soft vs hard sum-to-zero constrain for a simplex regression. The simulated data is really defined having incredibly low error [image] HARD 148.82 seconds (Total) mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat weights[1,1] -1.1458828 0.0005821308 0.007623225 -1.1599872 -1.1514000 -1.1455387 -1.1406438 -1.1312168 171.4891 0.9993008 weights[1,2] -0.4548668 0.0003671708 0.005209648 -0…

(This list might not be exhaustive.)