# Help needed for a constraint parameter problem

**URL:** <https://discourse.mc-stan.org/t/help-needed-for-a-constraint-parameter-problem/16417>\
**Category:** Modeling\
**Created:** [July 6, 2020, 6:10pm UTC](https://discourse.mc-stan.org/t/help-needed-for-a-constraint-parameter-problem/16417 "2020-07-06T18:10:32Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Samiran\_Sinha](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/samiran_sinha/32/5008_2.png) [@Samiran\_Sinha](https://discourse.mc-stan.org/u/Samiran_Sinha)\
**Post date:** [July 6, 2020, 6:10pm UTC](https://discourse.mc-stan.org/t/help-needed-for-a-constraint-parameter-problem/16417/1 "2020-07-06T18:10:32Z")

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Hello all,

Could you please help me to set the problem in rStan. Specifically, I want to know to how to write the .stan code for this problem. Many thanks for your help.

My observed data have a response vector Y and three predictor vectors X1, X2 and X3. Suppose that I want to fit a linear model, E(Y|X1, X2, X3)=beta\_0+beta\_1X1+beta\_2X2+beta\_3X3, with normal(0, sigma^2) measurement error.

The priors and the constrains are as follows: beta\_0~Uniform(-M, M) (denoted by U(-M, M)), beta\_1~U(-M, M), beta\_2~U(-M, M), beta\_3~U(-M, M), and log(sigma2)~U(-M, M), for some given M. Also, beta1+beta2+beta3=0.

The joint prior on beta\_1, beta\_2, beta\_3 can also be written as follows:  
z~discrete uniform distribution over indices 1, 2, 3.  
For r=1, 2, define [z+r]=z+r if z+r\<=3 else [z+r]=z+r-3.  
beta\_z~U(-M, M), beta\_[z+1]~U(max(-M,—M-beta\_z), min(M, M-beta\_z))  
beta\_[z+2]=-(beta\_z+beta\_[z+1]).

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**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/mike-lawrence/32/59_2.png) [@mike-lawrence](https://discourse.mc-stan.org/u/mike-lawrence)\
**Post date:** [July 8, 2020, 3:01pm UTC](https://discourse.mc-stan.org/t/help-needed-for-a-constraint-parameter-problem/16417/2 "2020-07-08T15:01:17Z")

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See here: [Defining a zero-sum constraint](https://discourse.mc-stan.org/t/defining-a-zero-sum-constraint/9007)

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**Author:** ![Samiran\_Sinha](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/samiran_sinha/32/5008_2.png) [@Samiran\_Sinha](https://discourse.mc-stan.org/u/Samiran_Sinha)\
**Post date:** [July 8, 2020, 8:58pm UTC](https://discourse.mc-stan.org/t/help-needed-for-a-constraint-parameter-problem/16417/3 "2020-07-08T20:58:30Z")

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Thanks Mike.