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### Jointly test coefficient is 0 across 3 outcomes from trivariate cross-classified model fitted using MCMC

Posted: Fri Mar 13, 2020 1:42 pm
Hi,

I've fitted a trivariate cross-classified model using MCMC.

I've been asked to calculate classical p-values for the joint test that a fixed-effect coefficient in the model equals 0 for all 3 dependent variables. For example, after fitting a nested model using RIGLS, I can use STATA command test to jointly test if the coefficient for covariate dr is 0 across the three dependent variables:

test dr_1 dr_2 dr_3

( 1) [FP1]dr_1 = 0
( 2) [FP2]dr_2 = 0
( 3) [FP3]dr_3 = 0

chi2( 3) = 310.87
Prob > chi2 = 0.0000

Is it okay to calculate this by hand for the trivariate cross-classified model (estimated using MCMC)? So using the relevant fixed effect estimates b and the relevant part of the fixed effect covariance matrix V I can calculate the chi-squared statistic as b*invsym(V)*b' and the get the 2-sided p-value from the the reverse cumulative chi-squared distribution with 3 degrees of freedom (e.g., 2*chi2tail(teststatistic)).

Is this a reasonable thing to do for a trivariate cross-classified model estimated using MCMC?

Thanks
Rach

### Re: Jointly test coefficient is 0 across 3 outcomes from trivariate cross-classified model fitted using MCMC

Posted: Fri Mar 13, 2020 4:26 pm
Hi Rachael,
MCMC is fitting a Bayesian model so the concept of a classical P value is not valid for MCMC estimates - I think we do offer Bayesian P values for all parameters though which basically check what proportion of iterations are positive / negative for a chain.
Best wishes,
Bill.