Compute ITT, TOT, and LATE with noncompliance

Within the same personalization experiment, some users assigned to the treatment never actually receive personalization, so there is noncompliance. You have the following user-level columns:

• Z (0/1): random assignment, used as the instrument
• D (0/1): whether personalization was actually received (the treatment received)
• Y (float): minutes streamed Tasks:

1. Define and calculate the Intention-to-Treat (ITT) effect of assignment on minutes streamed.
2. Explain what is usually meant by Treatment-on-the-Treated (TOT) in this context, and compute it.
3. Treating this as an instrumental variable, compute the LATE for compliers and state the assumptions needed.
4. Conceptually sort users into compliance groups (compliers, always-takers, never-takers, defiers) and indicate which group the LATE applies to. Overview: This question tests knowledge of causal inference and experimental analysis, especially estimating and interpreting ITT, TOT, and LATE when there is noncompliance, as well as classifying compliance types (compliers, always-takers, never-takers, defiers).