SOCI 620: Quantitative Methods 2

Location Onliine
Time Winter 2021, Tue and Thu 4:05–5:25pm
Instructor Peter McMahan
(
Office hours Wednesdays 1:30–3:00pm (via Zoom)
Lab sessions TBA
Syllabus https://soci620.netlify.com/

Description

As the second of two courses in the quantitative methods sequence, this class will introduce students to statistical techniques that extend and diverge from standard multivariate regression models. To this end, the course will have two main goals. First, students will become familiar with a range of quantitative methods common in social science research. Methodological topics will include generalized linear models for predicting categorical, ordered, and count data, multilevel/hierarchical linear models, and strategies for analyzing time-series and panel data. Students will learn to critically interpret these methods as they are used in the literature, and to utilize the methods for their own research.

The second goal of the course will be to provide students with an overarching framework to understand the methods we discuss as well as techniques they may encounter elsewhere. Instruction will therefore focus on a probabilistic interpretation of statistical models through a Bayesian lens. In addition to fostering a strong understanding of statistical dependence and parameter covariance, this approach will unify the methods we cover and enable students to build interpretable, theory-driven models of their own.

Requirements

Students are expected to be familiar with the readings, engage in discussions (in-class and/or online), complete assignments, and prepare an independent research project.

Class

The scheduled classes for the course will be hybrid lectures, discussions, and lab sessions. It is vital that students attend class regularly, having completed the readings and prepared to engage with the topics covered. If attending class is difficult or impractical for you (due to, e.g., time zone differences or Internet access), please get in touch with me as soon as possible to arrange accommodations.

Classes will be held online through Microsoft Teams. Slides and code will be made available before class, and lectures will be recorded and posted shortly after class.

Labs

In addition to the scheduled classes, we will have a weekly lab session (location to be determined). These sessions will be led by the T.A. as a space to practice techniques, raise questions and concerns, and discuss course content with one another. Attendance at these sessions is optional but strongly encouraged.

Equipment and software

We will be working with data and learning analysis and visualization in-class, so students must bring a laptop computer with them. Mobile devices such as tablets and phones, even with an external keyboard, will not be sufficient. If you do not have access to a laptop please talk to me as soon as possible so we can work out a way for you to participate.

We will be using the R statistical language and software for data processing, statistical estimation, and visualization in this class. It is recommended that students install the RStudio graphical interface, which I will be using for demonstration in class.

Readings

We will use the second edition of the textbook Statistical Rethinking by Richard McElreath for the course (McElreath 2020). I have put the book on reserve at the McLennan library building, and it is available for free online and as an ebook through the library website.

Assignments

There will be a short assignment due on most of the Thursdays of the semester (see the schedule for specific dates). These are intended to help you learn to use the methods we discuss in R and to give you practice in interpreting statistical models. Assignments should be submitted online through the Microsoft Teams site. Students can work together and consult one another on assignments, but each student should create their own, unique write-up for submission.

Independent research project

Each student will finish an independent research project by the end of the semester. These projects will be empirical, scholarly analyses, including a source of data, a well formed research question, a motivated statistical analysis, and a thorough interpretation of the results. Ideally, the projects will be related to work students are doing outside of class. Projects that represent a piece of a student’s broader research agenda are encouraged. The projects will be graded on the basis of four required assessments:

  1. Precis (Due March 9): This will be a short (no more than one page) description of the research project. It should include a specific research question, a brief description of the data that will be used, and an outline of the analytical strategy that will be employed. The purpose of the precis is to motivate the project and to establish its feasibility, not to perform any analyses or to answer any research questions.
  2. Proposal (Due March 30): Based on the feedback received from the precis, the project proposal will give a more detailed account of the research project. A good proposal will give a thorough account of the data that is being used, including some preliminary summaries and analyses. It will also articulate the research question in terms of statistical models and will specify those models formally.
  3. Presentation (In class, April 8 and 13): Each student will give a brief, PechaKucha-style presentation of their final project in class, consisting of twenty slides that will automatically advance ever twenty seconds. The presentation should describe your research question succinctly, give a clear account of the statistical model(s) used, and briefly interpret the results in light of the research question.
  4. Project write-up (Due April 21): The writeup for the final project will take the form of a formal scholarly paper. This should go into careful detail about the project, including a full description of the data, exposition and motivation of the statistical models used, a summary of the estimation of the model parameters, and a careful, thorough interpretation of the results. It should include tables and figures to illustrate your analysis.

Each student should arrange a brief meeting with me early in the term to discuss ideas for their research project and the appropriateness for the course.

Evaluation

The evaluation components and due dates for this course are strict. If outside circumstances will make it difficult to meet a requirement please raise the issue with me as soon as possible so we can find a solution. Regular absences will affect your ability to do well on assignments and the final project.

Item Due Weight
Assignments due dates listed on schedule 50% of final grade
Project precis March 9 5% of final grade
Project proposal March 30 10% of final grade
Project presentation March 30 10% of final grade
Project writeup April 21 25% of final grade

Accessibility

I strive to make the classroom as accessible as possible and to accommodate the particular needs of individual students. Students with disabilities in need of accommodation please contact the Office for Students with Disabilities (http://www.mcgill.ca/osd/, phone 514-398-6009) to work out a plan for meeting the course requirements. Students are encouraged to contact me with any further issues they may have attending class or completing the work.

Academic integrity

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offenses under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/students/srr/honest/ for more information).(approved by Senate on 29 January 2003)

L’université McGill attache une haute importance à l’honnêteté académique. Il incombe par conséquent à tous les étudiants de comprendre ce que l’on entend par tricherie, plagiat et autres infractions académiques, ainsi que les conséquences que peuvent avoir de telles actions, selon le Code de conduite de l’étudiant et des procédures disciplinaires (pour de plus amples renseignements, veuillez consulter le site http://www.mcgill.ca/students/srr/honest/).

Language of evaluation

In accord with McGill University’s Charter of Students’ Rights, students in this course have the right to submit in English or in French any written work that is to be graded. (approved by Senate on 21 January 2009)

Conformément à la Charte des droits de l’étudiant de l’Université McGill, chaque étudiant a le droit de soumettre en français ou en anglais tout travail écrit devant être noté (sauf dans le cas des cours dont l’un des objets est la maîtrise d’une langue).

Schedule

Background: probability and Bayesian statistics

Thu, Jan 7
Lectures:
Required:
  • (McElreath 2020, Ch. 1)

Tue, Jan 12
Lectures:
Required:
  • (McElreath 2020, Ch. 2)

Thu, Jan 14
Lectures:
  • Probability distributions and random samples
    (slides ;  video )
Required:
  • (McElreath 2020, Ch. 3)

Tue, Jan 19
Lectures:
Required:
  • (McElreath 2020, Ch. 4)

Linear models and model checking

Thu, Jan 21
Lectures:
  • Linear regressions from a Bayesian perspective
    (slides ;  video )
Required:
  • (McElreath 2020, Ch. 5)

Tue, Jan 26
Lectures:
Required:
  • (McElreath 2020, Ch. 6)

Thu, Jan 28
Lectures:
Tue, Feb 2
Lectures:
Required:
  • (McElreath 2020, Ch. 7)

Generalized linear models

Thu, Feb 4
Lectures:
Required:
  • (McElreath 2020, Ch. 10 and Section 11.1)

Tue, Feb 9
Lectures:
  • Logistic regression: methods and interpretation
    (slides ;  video )
Thu, Feb 11
Lectures:
Required:
  • (McElreath 2020, Section 11.2)

Tue, Feb 16
Lectures:
Required:
  • (McElreath 2020, Sections 12.1–12.2)

Thu, Feb 18
Lectures:
Required:
  • (McElreath 2020, Sections 11.3–11.5)

Tue, Feb 23
Lectures:
Required:
  • (McElreath 2020, Sections 12.2–12.5)

Data complications

Thu, Feb 25
Lectures:
Required:
  • (McElreath 2020, Ch. 15)

Break

Tue, Mar 2

Spring break — no class

Thu, Mar 4

Spring break — no class

Data complications (continued)

Tue, Mar 9
Lectures:
Due:
  • Final project precis

Multilevel models

Thu, Mar 11
Lectures:

Partial pooling of averages

Required:
  • (McElreath 2020, Section 13.1)

Tue, Mar 16
Lectures:
Required:
  • (McElreath 2020, Section 13.2)

Thu, Mar 18
Lectures:
Required:
  • (McElreath 2020, Section 13.4)

Tue, Mar 23
Lectures:
  • Covariance of coefficients and the LKJ prior
    (slides ;  video )
Required:
  • (McElreath 2020, Sections 14.1–14.2)

Thu, Mar 25
Lectures:
Required:
  • (McElreath 2020, Sections 14.3–14.4)

Due:
  • Final project proposal

Tue, Mar 30
Lectures:
  • (Canceled)
Required:
  • (McElreath 2020, Section 16.1)

Thu, Apr 1
Lectures:
  • Multilevel GLM and R formula specification
    (slides )
Due:
  • Problem set 5

Building more complex models

Tue, Apr 6
Lectures:
  • Time series and three-level and non-nested model
    (slides )
Required:
  • (McElreath 2020, Section 16.4)

Presentations

Thu, Apr 8

Student presentations

Tue, Apr 13

Student presentations

References

McElreath, Richard. 2020. Statistical Rethinking : A Bayesian Course with Examples in R and Stan. Second. Boca Raton : Chapman & Hall/CRC,.
Michael Betancourt. 2019. “Ordinal Regression.” May 2019. https://betanalpha.github.io/assets/case_studies/ordinal_regression.html.