Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 1, 65-81

VARIABLE SELECTION FOR REGRESSION MODELS

By

LYNN KUO
*University of Connecticut, Storrs*

and

BANI MALLICK
* Imperial College, London*

*SUMMARY.* A simple method for subset selection of independent variables in regression models is proposed. We expand the usual regression equation to an equation that incorporates all
possible subsets of predictors by adding indicator variables as parameters. The vector of indicator variables dictates which predictors to include.
Several choices of priors can be employed for the unknown regression coefficients and the unknown indicator parameters.
The posterior distribution of the indicator vector is approximated by means of the Markov Chain Monte Carlo algorithm. We select subsets with high posterior probabilities. In addition to linear models, we consider generalized linear models.

*AMS (1991) subject classification. *62JO5, 62J02.

*Key words and phrases. *Bayesian inference, F-tests, generalized linear model, Gibbs sampling, linear model, subset selection.