It is tempting to interpret, as opposed to analyze, poetry text from the perspective of one's current historical, social, or cultural era and personal experience (interpretation can often reduce to extrapolations of meaning from one's own personal experience). While this might be useful with some texts, perhaps with Contagion by Robin Cook or Extremely Loud & Incredibly Close by Thomas Schell, it is counterproductive with other texts, especially so with works having universal themes.
It can also be counterproductive to finding understanding to analyze texts without due attention carefully paid to syntax and punctuation structures: a semicolon versus a colon can radically alter the meaning of written text; this is why writers use them with such selective care (although styles of punctuation alter periodically and must be understood within their historic time frame to avoid confusion).
Christina Rossetti has been generally acknowledged by readers and critics alike to write "poetry displaying a perfection of diction, tone, and form" (PoetryFoundation.org). It is also acknowledged that Christina wrote on recurring ideas of the "inconstancy of human love, the vanity of earthly pleasures, renunciation, individual unworthiness, and the perfection of divine love [as] recurring themes in her poetry" (PoetryFoundation.org).
Thus, in consideration of these two aspects of her work--structure and theme--in order to fully understand Rosetti's work a two-fold approach to analysis is needed. Bear in mind that "analysis" can be very different from and yield very different results to "interpretation." Interpretation of a literary work may arise from one's personal experience, one's culture, one's society, one's historical period, or one's emotional response (which may or may not be related to direct personal experience, for example the emotional response elicited when watching The Blind Side though most of us are not underprivileged high school football players). Examples of these kinds of interpretation might be reading Oliver Twist through your own experience of poverty; reading "Remember" by Christina Rosetti through your own cultural norms; reading The Red and the Black through your own social-religious structure; reading Pride and Prejudice through the eyes of a 19th century Marxist; or reading Evelina by Fanny Burney according to your own emotional response.
In general, analysis of literature applies more structured application of logic than these interpretive approaches do, although there are literary criticism approaches that incorporate interpretive elements, such as Reader-Response Criticism and Marxist Criticism. What is the advantage of either analysis or interpretation over the other?
The advantage of analysis over interpretation is that analysis helps us understand, as much as possible, what the author was expressing. Some think this is the most advantageous way to know what literature illustrates (illustrates rather than suggests) about human nature, the pitfalls of living, the nature of life, the pain of death, and metaphysical hopes.
To illustrate this concept of advantage, if Crime and Punishment is about a student who becomes obsessed with the philosophical notion of the "superman" who is above the regulating norms of life, that has little bearing on the majority of people that ever were or ever will be since most of us are not thus obsessed. Yet if Crime and Punishment is about a student who has an altruistic heart motivated by pity and anguish who literally and figuratively throws himself into his neighbors' fires thereby depriving himself of what is required for the sustenance of life and sanity, that could very well be applicable to many overly-large-hearted students anywhere in the world. Analysis rather than interpretation will identify which of these themes is the driving force in the text.
In order to accurately understand the complex form and structure of "Remember," a two-pronged analysis approach is needed to identify theme and meaning. For meaning, the close reading and formal analysis of New Criticism is needed to understand syntax and the distinctions in meaning made by punctuation. For theme, the application of the principles of Historical Criticism (also called Traditional Criticism), which keeps touch with the author by examining biography and society, is needed.