SOCI 620: Quantitative Methods 2

Location Leacock 834
Time Winter 2023, Tue and Thu 8:35–9:55am
Instructor Peter McMahan
()
TA Khandys Agnant
Office hours Thursdays, 4pm–5pm (Leacock 727)
Work sessions TBA
Syllabus https://soci620.netlify.app/

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 parametric estimation, 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 during class (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 instructor-led lab sessions. It is vital that students attend class regularly, having completed the readings and prepared to engage with the topics covered.

Currently, classes are scheduled to be held live in person. Slides and code will be made available before class. Lectures will be live-streamed on Teams (when necessary), and recordings will be posted shortly after class.

Note: While in-person participation provides a much better learning experience, the current pandemic may make physical co-presence impractical or unsafe for certain students. Online participation will be possible with the consent of the instructor. In all cases, the health and safety of the students, their families, and the community at large will take precedece.

Work sessions

In addition to the scheduled classes, we will have a weekly work 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). The book is available as an ebook through the library website. If you are unable to access the textbook, please let me know as soon as possible.

Worksheets

There will be four worksheets due throughout 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 Thu, Mar 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 Thu, Mar 23): 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 (Due Thu, Apr 6): 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. (Details on final presentation format)
  4. Project write-up (Due Fri, Apr 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.

Note: In the event of extraordinary circumstances beyond the University’s control, the content and/or evaluation scheme in this course is subject to change

Worksheets See schedule for dates 44% of final grade
Project précis Thu, Mar 9 5% of final grade
Project proposal Thu, Mar 23 10% of final grade
Project presentation Thu, Apr 6 16% of final grade
Project writeup Fri, Apr 21 25% of final grade

Accessibility and accommodation

Students who need accommodation or who are having trouble accessing any aspect of the course may contact me directly. I will make every effort to accommodate individual circumstances—including religious, medical, or other personal circumstances.

Students with disabilities in need of formal accommodation are encouraged to contact the Office for Students with Disabilities (http://www.mcgill.ca/osd/, phone 514-398-6009).

Les étudiants qui ont besoin d’un accommodation ou qui ont des difficultés à accéder à un aspect du cours peuvent me contacter directement. Je ferai tout mon possible pour tenir compte des circonstances individuelles, y compris des circonstances religieuses, médicales ou autres.

Les étudiants handicapés ayant besoin d’un accommodation formel sont encouragés à contacter le Bureau des étudiants en situation de handicap (http://www.mcgill.ca/osd/fr, téléphone 514-398-6009).

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 5
Lectures:
Required:
  • (McElreath 2020, Ch. 1)

Tue, Jan 10
Lectures:
  • Probability models of social processes
    (slides )
Required:
  • (McElreath 2020, Ch. 2)

Thu, Jan 12
Lectures:
  • Probability distributions and random samples
    (slides )
In-class lab:
  • Approximating simple posteriors cont’d: Working with random samples

Required:
  • (McElreath 2020, Ch. 3)

Tue, Jan 17
Lectures:
  • Multi-parameter posteriors
    (slides )
Required:
  • (McElreath 2020, secs. 4.1–4.3)

Linear models and model checking

Thu, Jan 19
Lectures:
  • Linear regressions from a Bayesian perspective
    (slides )
Required:
  • (McElreath 2020, Sec 4.4-4.7)

Supplementary:
  • (McElreath 2020, Ch. 5)

Due:
Tue, Jan 24
Lectures:
  • Covariates for causal analysis
    (slides )
Required:
  • (McElreath 2020, Ch. 6)

Thu, Jan 26
Lectures:
  • Checking models and estimates
    (slides )
Tue, Jan 31
Lectures:
  • Parsimony and overfitting
    (slides )
Required:
  • (McElreath 2020, Ch. 7)

Generalized linear models

Thu, Feb 2
Lectures:
  • Logistic regression: motivation
    (slides )
Required:
  • (McElreath 2020, Ch. 10 and Section 11.1)

Tue, Feb 7
Lectures:
  • Logistic regression: methods and interpretation
    (slides )
Thu, Feb 9
Lectures:
In-class lab:
Required:
  • (McElreath 2020, sec. 11.2)

Tue, Feb 14
Lectures:
  • Expanding on Poisson regressions
    (slides )
Required:
  • (McElreath 2020, secs. 12.1–12.2)

Due:
Thu, Feb 16
Lectures:
Required:
  • (McElreath 2020, secs. 11.3–11.5)

Tue, Feb 21
Lectures:
  • Cumulative probability and ordinal outcomes
    (slides )
Required:
  • (McElreath 2020, secs. 12.2–12.5)

Supplementary:
  • Ordinal regressions (Michael Betancourt 2019)

Complications in data and estimation

Thu, Feb 23
Lectures:
  • MCMC and assessing convergence
    (slides )
In-class lab:
Required:
  • (McElreath 2020, Ch. 9)

Due:
  • Worksheet 3
Tue, Mar 7
Lectures:
Required:
  • (McElreath 2020, Ch. 15)

Thu, Mar 9
Lectures:
In-class lab:
Due:
  • Project précis

Multilevel models

Tue, Mar 14
Lectures:
  • Nested data and partial pooling
    (slides )
Required:
  • (McElreath 2020, sec. 13.1)

Thu, Mar 16
Lectures:
In-class lab:
Required:
  • (McElreath 2020, sec. 13.2)

Tue, Mar 21
Lectures:
  • Introduction to random slopes
    (slides )
Required:
  • (McElreath 2020, sec. 13.4)

Thu, Mar 23
Lectures:
  • Covariance of coefficients and the LKJ prior
    (slides )
Required:
  • (McElreath 2020, secs. 14.1–14.2)

Due:
  • Project proposal
Tue, Mar 28
Lectures:
  • Two-level models in detail
    (slides )
In-class lab:
Required:
  • (McElreath 2020, secs. 14.3–14.4)

Thu, Mar 30
Lectures:
  • Multilevel GLM and R formula specification
    (slides )
In-class lab:
Due:
  • Worksheet 4

Building more complex models

Tue, Apr 4
Lectures:
  • Time series, three-level, and non-nested models
    (slides )
Required:
  • (McElreath 2020, sec. 16.4)

Presentations

Thu, Apr 6

Student presentations 1

Due:
  • Project presentation
Tue, Apr 11

Student presentations 2

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.