This book explores the concept of complementation in the adjectival domain of English grammar. Alternation between non-finite complements, especially to infinitives and gerundial complements, has been investigated intensively on the basis of large corpora in the last few years. With very few exceptions, however, such work has hitherto been based on univariate analysis methods. Using multivariate analysis, the authors present methodologically innovative case studies examining a large array of explanatory factors potentially impacting complement choice in cases of alternation. This approach yields more precise information on the impact of each factor on complement choice as well as on interactions between different explanatory factors. The book thus presents a methodologically new perspective on the study of the system of non-finite complementation in recent English and variation within that system, and will be relevant to academics and students with an interest in English grammar, predicate complementation, and statistical approaches to language.