Hi I would like to use Stan to estimate a regression model with inequality constraints on linear combinations of parameters. Here is a simplified example, a quadratic function: y_i = \beta_0 + \beta_1 x_{1,i} + \beta_2 x_{2,i} + 0.5 \beta_{11} x_{1,i}^2 + \beta_{12} x_{1,i} x_{2,i} + 0.5 \beta_{22…

[image] Arne_Henningsen: If I use priors with very low probabilities for values close to zero, e.g.: dydx1 ~ lognormal( log(0.8), 1 ); dydx2 ~ lognormal( log(0.8), 1 ); there are no longer divergent transitions after warmup but the estimates are largely driven by the (quite ‘spiky’) priors…

transformed parameters{ real<lower=0.1,upper=0.6>[N] t_1 = parametric_function_1; real<lower=0.1,upper=0.6>[N] t_2 = parametric_function_2; } Unfortunately, this method can cause Stan to hang or to random walk because it only rejects unsuitable parameters, rather than retroactively restricting the …

[image] Corey.Plate: transformed parameters{ real<lower=0.1,upper=0.6>[N] t_1 = parametric_function_1; real<lower=0.1,upper=0.6>[N] t_2 = parametric_function_2; } Unfortunately, this method can cause Stan to hang or to random walk because it only rejects unsuitable parameters, rather than retro…

I might have gotten a little closer to a solution: setting priors on the partial derivatives (transformed parameters). If I use priors with very low probabilities for values close to zero, e.g.: dydx1 ~ lognormal( log(0.8), 1 ); dydx2 ~ lognormal( log(0.8), 1 ); there are no longer divergent t…

[image] Arne_Henningsen: We have prior knowledge that the partial derivatives of y_i with respect to x_{1,i} and x_{2,i} are non-negative for all observations i = 1, …, N: Hi, @Arne_Henningsen . [image] martinmodrak: In principle, given x you should be able to solve for absolute lower and…

[image] martinmodrak: [image] Arne_Henningsen: If I use priors with very low probabilities for values close to zero, e.g.: dydx1 ~ lognormal( log(0.8), 1 ); dydx2 ~ lognormal( log(0.8), 1 ); there are no longer divergent transitions after warmup but the estimates are largely driven by …

[image] Bob_Carpenter: [image] Arne_Henningsen: We have prior knowledge that the partial derivatives of y_i with respect to x_{1,i} and x_{2,i} are non-negative for all observations i = 1, …, N: Hi, @Arne_Henningsen . [image] martinmodrak: In principle, given x you should be able to s…

If somebody is interested in the code that uses ‘soft constraints’, it is available at GitHub ( GitHub - arne-henningsen/Stan_inequality: Inequality constraints in Stan ) and here: Stan_inequality.R: # load required package(s) library( "miscTools" ) library( "rstan" ) # number of observations (befo…

[image] Arne_Henningsen: Therefore, I am concerned that defining the lower bound of \beta_1 based on the currently sampled values of \beta_{11} and \beta_{12} creates sampling problems. This is not how variables work in Stan. Sampling happens on the unconstrained scale and if the constraints…

Inequality constraints on linear combinations of parameters

Modeling

andrjohns March 18, 2025, 4:29am 3

It might not be completely applicable to your model, but there are some previous examples/discussions of inequality constraints here: Simple normal regression model with inequality constraints on the parameters

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Inequality constraints on linear combinations of parameters

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