In parsing, the identification of thematic roles not only is fundamental to semantic interpretations but also can reduce syntactic branches and ambiguities. Since the syntactic structures for natural languages are usually complicated and ambiguous, there is no uniquely deterministic parsing strategy. This paper observes that, in addition to real world knowledge, there are four parameters to identify the roles of constituents in a sentence. They are syntactic categories and semantic features of constituents, case frames and case restrictions of verbs, syntactic configurations and word order, and obligue case assigners. Further, this paper shows how the parameters, including syntactic and semantic information, are represented in feature structures, and how they function in identifying thematic roles. The thematic roles of constituents can be determined by accumulating parametric information. Thus, it is believed that the unification parsing strategy can make parsing more deterministic and efficient.