## one-tailed test for a predictor in MCMC

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### one-tailed test for a predictor in MCMC

This may be a naive question as I am not a statistician. I am doing an MCMC analysis to determine whether a variable (intervention or control group) is a significant predictor of a binary outcome. I can add this variable as a predictor in the MCMC model and see if there is any improvement to the DIC to determine whether it is a significant predictor of the outcome, which I believe is a two-tailed test at 5% significance level. I think I am justified in doing a one-tailed test as the effect will only really go in one direction, but how can i do this in MLwin?

sianphillips

Posts: 7
Joined: Thu Aug 04, 2011 11:33 am

### Re: one-tailed test for a predictor in MCMC

Hi Sian,
I think you are a little confused here. The DIC diagnostic is an information criterion that can be used to compare models in a similar way to the AIC and BIC in a non-Bayesian/MCMC setting. What it is not is equivalent to 'a two-tailed test at 5% significance level'. The closest thing in the Bayesian MCMC world to the test you are asking is to compare the parameters interval estimates with the value 0. So if you were say wanting to see if parameter beta_2 is significant at the 5% level then you could click on it's trajectory to get MCMC diagnostics. Here you will get quantiles of it's distribution and looking at the 2.5% and 97.5% quantiles gives a 95% interval estimate for beta_2. If this interval doesn't contain 0 i.e. both quantiles have the same sign then this suggests significance (2-sided) at the 95% level. If you wish to look at one-sided then depending on direction one would look at the 5% or 95% quantile and see if it is the correct side of 0 i.e. if you are testing versus beta_2 > 0 then look at 5% quantile and whether it is positive if beta_2 < 0 then look at 95% quantile and whether it is negative.
Hope this makes sense.
Bill.
billb

Posts: 19
Joined: Fri May 21, 2010 2:21 pm

### Re: one-tailed test for a predictor in MCMC

Dear Bill,

Thank you very much, thats just what i needed to know

Thanks again,
Sian
sianphillips

Posts: 7
Joined: Thu Aug 04, 2011 11:33 am