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- PROC MCMC Multivariate t Prior in Mixed Model

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03-07-2016 02:06 PM - edited 03-07-2016 02:06 PM

Hi all,

I was wondering if anyone has tried to specify a multivariate t distribution for the fixed effects in a mixed model. I have some code below that I used to fit a model to some simulated data. In this code, I assumed a multivariate normal prior on the beta's. Does anyone know whether or not I can specify a multivariate t? I looked into the GENERAL statement in PROC MCMC where you can specify custom distributions. Does it look like I'll have to use GENERAL?

```
proc mcmc data = SimulatedData;
array theta[2] b0 b1;
array theta_c[2];
array mu0[2] (0,0);
array sigma_c[2,2];
array sigma_0[2,2] (10000 0 0 10000);
array s[2,2] (0.02 0 0 20);
parms theta_c sigma_c {.1 0 0 .1} var_y;
prior theta_c ~ mvn(mu0, sigma_0);
prior sigma_c ~ iwish(2, s);
prior var_y ~ igamma(0.01, scale = 0.01);
random theta ~ mvn(theta_c, sigma_c) subject = Subject;
mu = b0 + b1*Time;
model Response ~ Normal(mu, var = var_y);
run;
```

Thanks.

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03-07-2016 02:28 PM

I'n not an expert on MCMC, but there are two places in the doc that seem relevant. The first is that the multivariate t distribution is not one of the built-in multivariate distributions that are supported by PROC MCMC. The second is in the section on sampling methods where it states that you can specify a t distribution on the PARMS statement multidimensional parameters.

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03-07-2016 02:35 PM

Yes, multivariate t is not one of the recognized distributions. I tried specifying a t-distribution on the PARMS statement but that did not lead to the goal of specifying a multivariate t on the fixed effects. I am currently trying to use the GENERAL statement to specify a custom multivariate t. Have you had any experience with this?

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03-07-2016 02:49 PM

No, I have no experience with this. However, Zhang (2013, p. 16-17) shows how to use generalized error distributions in PROC MCMC by using the GENERAL statement. Perhaps that will be helpful for you.