Attribute is a dependent element of a nominative phrase that denotes an attributive quality of an object expressed by a noun. It is a secondary part of the sentence modifying a part of the sentence expressed by a noun, a substantival pronoun, a cardinal numeral, and any substantivised word, and characterizing the thing named by these words as to its quality or property. According to the position relative to the head word, attributes can be prepositive and postpositive. The position of an attribute with respect to its head word depends partly on the morphological peculiarities of the attribute itself, and partly on stylistic factors. Apposition has been often regarded as a special kind of attribute, and sometimes as a secondary part of a sentence distinct from an attribute. Apposition is a word or phrase referring to a part of the sentence expressed by a noun, and explaining and specifying its meaning by giving it another name. Appositions are usually expressed by nouns. The major problem concerning the secondary sentence parts is caused by the fact that characteristic features of each of the three types are not clearly defined, therefore describing a given word or phrase as an object or an attribute in some cases, or describing it as an object or an adverbial modifier, in others, often proves to be a matter of personal opinion or predilection. There are some elements of the sentence which are neither its main parts, nor any of the usual secondary ones. They are the direct address and the parenthesis. (Refer to the book by Ilyish for more information).
