The poem's use of anaphora adds authority and a sense of exacerbated insistence to the speaker's tone. That anaphora itself is subtle, however; the most commonly repeated word ("Nobody") is only used a total of six times (so once per stanza, on average), and after the first two times, which happen successively, the anaphora is interrupted by sentences and even entire stanzas in which anaphora doesn't appear. (In fact, one might argue that after the first stanza, the recurrence of the word "Nobody" is just regular repetition and not anaphora at all.)

Despite the anaphora only being used heavily in the first stanza of the poem, the effect of it is huge. By front-loading the poem with the repetition of the word "nobody," the poet sets up an expectation for this kind of insistent denial that the reader feels echoing throughout the rest of the poem, even though sentences vary more often than not.

The repetition of the word "Nobody" has somewhat of a haunting effect as well. The parents deny the accuracy of their child's memories, but rather than saying "we didn't do that" or "so-and-so didn't do that," they use the word "Nobody." Somehow this phrasing is more ambiguous, more evasive than if they were to say "I didn't do that" or "that's not how I remember it."

There are also smaller moments of anaphora with the repetition of "we," as in:

[...] we have the facts. We called the tune.

And:

We did what was best. We remember your childhood well.

This anaphora places repeated emphasis on the parents' point of view and authority.