[R] Prediction interval of Y using BMA

From: <Nicolas.Meyer_at_chru-strasbourg.fr>
Date: Thu 13 Jul 2006 - 02:48:54 EST

Hello everybody,

In order to predict income for different time points, I fitted a linear model with polynomial effects using BMA (bicreg(...)). It works fine, the results are consistent with what we are looking for. Now, we would like to predict income for a future time point t_next and of course draw the prediction interval around the estimated value for this point t_next. I've found the formulae for the ponctual estimation of t_next but I cannot succeed in finding the formula to compute the prediction interval based on BMA sets of models, which requires the adequate variance. The paper of Hoeting et al. on BMA gives the posterior variance of a parameter but what I want is the posterior variance of a predicted Y and not the posterior variance of a beta, since the goal here is not to build an explanatory model but an accurately predictive model. Is there a way to get around it with the function of the BMA package or does anybody has indication on where to find the formulae ? I searched the web for hours but nothing like this is to be found. Any help will be appreciated.
Thank's in advance,      

Nicolas Meyer
Département de Santé Publique
Unité de Biostatistique et Méthodologie
03 88 11 63 58
nicolas.meyer@chru-strasbourg.fr <mailto:nicolas.meyer@chru-strasbourg.fr>  

La conjecture de Feynman :
"To report a significant result and reject the null in favor of an
alternative hypothesis is meaningless unless the alternative hypothesis has been stated before the data was obtained"
"The meaning of it all", 1998.

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