Moreover , in order to determine whether the performances of the predictive criteria are consistent across different learning models within the same domain , we have performed the study on two parsing models : one based on a context-free variant of tree-adjoining grammars ( Joshi , Levy , and Takahashi 1975 ) , the Probabilistic Lexicalized Tree Insertion Grammar ( PLTIG ) formalism ( Schabes and Waters 1993 ; Hwa 1998 ) , and Collins 's Model 2 parser ( 1997 ) .