Collostructional analysis is a corpus-based quantitative method of measuring the mutual attraction of lexemes and constructions (cf. Stefanowitsch and Gries 2003) which has gained considerable popularity among corpus linguists and especially cognitive linguists with a statistical bent. For many less statistically minded linguists, it has proven rather difficult to evaluate the theoretical background assumptions and cognitive underpinnings of collostructional analysis and to compare them to alternative ways of modelling lexicogrammatical attraction phenomena. This paper aims to spell out these premises and foundations in terms comprehensible to a wider audience. It begins with a concise survey of how collostructional analysis works and then reports on a number of practical, theoretical and statistical issues of which both practitioners of the method and those who try to appreciate results of its application should be aware. With these issues in mind we then discuss alternative ways of calculating and interpreting lexicogrammatical attraction. The advantages and disadvantages of the different methods are discussed, also against the background of the results of studies that have tried to evaluate the measures by means of external evidence from psycholinguistic experiments. Finally, cognitive underpinnings of lexicogrammatical associations and implications for the different approaches are discussed. It is argued that at present we lack adequate knowledge about the ways in which discourse frequencies affect entrenchment. We conclude that the complexities of the relation between corpus frequencies and degrees of entrenchment are still rather poorly understood, and make suggestions for future work.
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