Homework 6

Due Sunday, October 11 at midnight CST on Moodle

Please turn in two PDF documents from class exercises.

(If you have LaTeX installed, you can knit directly to PDF (preferred method). Otherwise, you can knit to HTML and “Print” the page to save it as a PDF.)


Deliverables

Please turn in exercises from the following class days:

  • Topic 17: Applied Mediation Analysis
  • Topic 18: Instrumental Variables Analysis

This should be a total of two PDF documents.


Primary objectives

The following learning objectives are the primary focus of this assignment:

  • DSEP1: Apply d-separation to block noncausal paths in causal DAGs with and without unobserved variables.
  • MEDI1: Formulate research questions that can be answered via mediation analysis
  • MEDI2: Conduct and interpret results from a mediation analysis
  • IVAR1: Design and evaluate an instrumental variables study in light of the instrumental variables assumptions.
  • IVAR2: Explain how instrument strength and analysis choices affect the results of an instrumental variables analysis


Revisiting previous objectives

You can revisit any of the following objectives (excludes REGR1, IPTW1) by incorporating them within the context of the assignment as below.

> **Revisiting objective DESI1:** Enter a response here that demonstrates that you show solid understanding of the DESI1 objective within the context of this assignment.
  • EXCH1: Apply the concepts of marginal and conditional exchangeability to answer questions about (hypothetical) data on potential outcomes.
  • EXCH2: Give examples of when marginal and conditional exchangeability would and would not hold in various data contexts.
  • EXCH3: Explain why a direct comparison of the outcomes in the treated and untreated is misleading as an estimate of a causal effect.
  • DESI1: Explain how randomized experiments relate to exchangeability.
  • DESI2: Explain how quasi-experimental and general observational studies relate to exchangeability.
  • DESI3: Compare the strengths and weaknesses of different study designs for answering a research question.
  • PGRA1: Apply the Causal Markov assumption to express the joint distribution of data.
  • CNCP1: Explain how causal and noncausal paths relate to exchangeability and causal effects.
  • DSEP2: Apply strategies to deal with exchangeability problems caused by unobserved variables.
  • DSEP3: Simulate data from a causal DAG under linear and logistic regression SEMs to check d-separation properties through regression modeling and visualization.
  • DSEP4: Explain how d-separation relates to conditional exchangeability.
  • TVTR1: Formulate research questions that can be answered in a time-varying treatment setting.
  • TVTR2: Explain why regression does not generally work in time-varying settings with treatment-confounder feedback using d-separation ideas.


For the following objectives, you will have opportunities to revise your responses on Homework 5 based on feedback, so do not include these objectives in any revisits you do for this assignmemt.

  • SENS1: Evaluate the sensitivity of findings to data quality and propose appropriate sensitivity analyses for a research investigation
  • SENS2: Conduct and communicate the results of a sensitivity analysis for unmeasured confounding.
  • DISC1: Demonstrate conceptual understanding of causal discovery by reasoning about outputs of the process and by manually conducting it using regression models.
  • DISC2: Use output from causal discovery to enhance a causal analysis as part of a sensitivity analysis.