The pronoun shifts signify change in point of view, and also illustrate Marian's vascillating relation with reality and self.
In the first section, the pronouns are in the first person. Marian is telling her story from her own point of view, as if she were talking to herself.
In the second section the pronouns are in the third person. Following her engagement, Marian grows increasingly detached from herself and her life situation. She leaves all decision-making to Peter, and begins to lose a clear sense of reality and of who she is. The use of a more detached third person perspective works well in accentuating Marian's separation from self and consequent descent into eating disorder.
In the final section of the book, Marian separates from Peter, regains her hold on reality, and notes, "I was thinking of myself in the first person singular again". The pronouns and perspective shift accordingly.