Here is the sentence from OG17 Diagnostic Test Reading Comprehension Passage 1.
According to economic signaling theory, consumers may perceive the frequency with which an unfamiliar brand is advertised as a cue that the brand is of high quality.
I have been perplexed by the structure of this sentence and the usage of which.
Here is my thought. The main structure is
Consumers(Subject) perceive(Verb) the frequency(Object) as a cue(Complement).
Here is my question.
What the role of 'which' in the sentence. Is it a relative pronoun?
Why there is a preposition(with) preceding 'which'? What is the role of 'with' in the sentence?
Also, what is the role of the word that in the sentence 'that the brand is of high quality'.
Thank you!