The effectiveness of literary, or stylistic, devices like metaphor and allusion depends upon knowledge the reader brings to reading the text. If my Greek mythology is weak, a Classical allusion to Scylla and Nisus will persuade me of nothing, only confuse and distract me. Similarly, the metaphor "her presence was a Himalayan breeze" will persuade me of nothing unless I know geography and the climate and air quality in the Himalayas. So let us assume readers are knowledgeable about these and human experience, which is what personification depends upon.
The following excerpt from Pope’s The Rape of the Lock contains Classical allusion and can be examined to see how analysis shows how a reader might be persuaded by it.
Clarissa drew with tempting Grace
A two-edg'd Weapon from her shining Case;
So Ladies in Romance assist their Knight,
Present the Spear, and arm him for the Fight.
He takes the Gift with rev'rence, (Canto III)
Pope employs chivalric allusion to the era of knights and chivalry. The allusions are "drew ... a two-edged Weapon from her ... Case," "in Romance assist their Knight," "present the spear," "arm him for the Fight," and "takes the gift with reverence."
The first step to analyzing this for persuasion is to identify the allusions. If readers were to take these phrases literally, they'd be very confused. They'd picture a knight in shinning armor in the middle of a parlor in 1712 amidst boisterously dressed women with enormous skirts: a most incongruous image. They would also envision a petticoat clad woman draw a weapon from her "Case," as though she too were a warrior.
Therefore, the second step to analyzing whether this allusion is persuasive is to determine if there are textual clues to alert the reader to the presence and meaning of the allusions.
One clue is that the whole context is satirically humorous and ironic. At no point is anything to be taken for what it literally says. Everything has an unstated figurative meaning. Another clue is the vocabulary that tells readers Pope is being satirical and ironic: e.g., "tempting Grace," these words contradict each other, setting up irony; "her shinning Case," a warrior lady might have a polished scabbard but not a "shinning Case"; "So Ladies in Romance assist" indicates a mock portrayal of what ladies of old did. This analysis indicates that--since the whole tends to figurative language and meaning underlying irony and satire--the mention of Knights and shinning Cases is also figurative and hence an allusion to a time of old.
Analysis for things like metaphor would follow the same procedure by examining the text for diction, vocabulary, irony, tone, mood (the same as atmosphere), other figurative language as well as illustration of statements and imagery. If, for example, our Himalayan metaphor were followed by "cool" and "fresh" or by the comparative simile "as welcome as air to a bird," which illustrate through vocabulary and imagery, then you may determine the metaphor to be persuasive to readers.
Devices like personification and imagery depend upon life experience instead of knowledge. The third step in analysis to show if these devices persuade readers is to evaluate whether they are true to human experience. For example, the personification, "the plaster wall reeled joyfully," might be judged not in keeping with human experience, therefore not persuasive. These are steps in analyzing literary, or stylistic, devices for if they persuade readers.