Many current approaches to statistical language modeling rely on independence a.~sumptions 1)etween the different explanatory variables. This results in models which are computationally simple, but which only model the main effects of the explanatory variables oil the response variable. This paper presents an argmnent in favor of a statistical approach that also models the interactions between the explanatory variables. The argument rests on empirical evidence from two series of experiments concerning automatic ambiguity resolution. .