Analogies can be classified based on the type of relationship they present. There are four main relationship types tested on the MAT: semantic, classification, association, and logical/mathematical. For in-depth coverage, I suggest reading through the official MAT study guide.
MAT Relationships: Semantic
Semantic analogies create relationships based on the literal definition of the terms given. The terms are linguistically connected and may represent synonyms, antonyms, or other types of definition based connections:
Vacillate : Waver (Both words mean to be indecisive.)
Breeze : Squall (A squall is a violent wind; these represent different levels of intensity for the same concept.)
Amenable : Pugnacious (Amenable is friendly; in contrast, pugnacious refers to a standoffish, disagreeable person.)
MAT Relationships: Classification
Classification relationships are based on either both terms belonging to the same category, or else one term is contained within another:
Emotion : Joy (Joy belongs in the class or category of emotions.)
Wolf : Jackal (Both wolves and jackals belong in the same genus — Canis.)
Girder : Building (A girder is part of a building.)
MAT Relationships: Logical/Mathematical
This relationship features logical or mathematical equations, numerical fractions, multiples, negation, or letter and sound patterns.
1/2 : 1/20 (1/2 is 10 times as much as 1/20.)
7 : 11 (7 and 11 are consecutive prime numbers.)
Rant : Slant (Rant and slant rhyme.)
MAT Relationships: Association
Association relationships deal with two distinct but related ideas. In a sense, this is a catch all category featuring any relationship that would not fit neatly into the other three.
Snake : Scales (A snake has scales.)
Hurricane : Damage (A hurricane typically produces damage.)
Deaf : Hearing (To be deaf is to lack hearing.)
More on relationships
This is just a quick overview of the types of analogy relationships featured on the MAT. For more information, see the MAT Official Guide. I would also suggest looking at some of our relationship-specific blogs, such as MAT semantic analogies. You can also try your hand at over 100 practice questions using the Miller Analogies flashcard app (free).