  We consider a problem of linear model selection in the presence of both
continuous and categorical predictors. Feasible models consist of subsets of
numerical variables and partitions of levels of factors. A new algorithm called
delete or merge regressors (DMR) is presented which is a stepwise backward
procedure involving ranking the predictors according to squared t-statistics
and choosing the final model minimizing BIC. In the article we prove
consistency of DMR when the number of predictors tends to infinity with the
sample size and describe a simulation study using a pertaining R package. The
results indicate significant advantage in time complexity and selection
accuracy of our algorithm over Lasso-based methods described in the literature.
Moreover, a version of DMR for generalized linear models is proposed.
