About the Course


  • Randi Garcia (rgarcia@smith.edu, Bass 415, 413-585-3698). Randi’s office hours will be held on Tuesdays from 10:00a-11:00a, and Thursdays from 1:00p-3:00p, or by appointment.


This course introduces students to applied data analysis using Structural Equation Modeling (SEM), a multivariate statistical approach that allows for simultaneous estimation of coefficients from multiple, related, linear models. With SEM, complex theories can be tested wherein a construct is a response variable, but also is a predictor of another construct. Students in this course will develop a fundamental understanding of strategies for model specification, identification, estimation, and determining model fit. Topics will include factor analysis, latent variable modeling, mediation analysis, measurement invariance testing, and latent growth curve modeling. Emphasis will be placed on the practical applications of SEM and latent variable techniques to address relevant questions in psychology, education, government, and the social sciences more broadly. We will use R computing software.

Prerequisites: Introductory statistics and SDS/MTH 291: Multiple Regression.

Course Goals
  • Recognize and specify structural equation models that relate to theoretical models.
  • Assess issues with proposed models incuding model fit, identification, and other specification issues.
  • Assess the soundness of fitted models with respect to causal propositions and statistical assumptions in your own and others work.
  • Communicate orally about decisions made and the trade-offs faced during your own model specification and re-specification.
  • Write up the results of structural equation models in manuscript results sections.


  • Principles and Practice of Structural Equation Modeling Rex B. Kline, 3rd edition

The textbook is not just a reference to use after the instructor has presented new material but a sourcebook to use at every stage of learning. When all students read the text before class, the nature of the class meeting changes to the benefit of everyone. You will have thought about the material, and you will arrive with your own questions. You’ll be ready to discuss what you understand, to clarify what you don’t understand, and to hear more on the topic. You need to read the book prior to class as well as review the material after we’ve discussed it in class.


Classes meet Monday and Wednesday in Bass 002. Most Mondays will be discussion and activity based learning of basic concepts, while most Wednesdays will be devoted to working on guided in-class lab assignments (see below). Your participation is an important part of the learning process. If you cannot attend a particular class I would appreciate the courtesy of advanced notice and an explanation for your absence. Class participation and attendance contribute 10% to your final grade.

I hope it goes without saying, but while the class is in session, you should not use your computer or cell phone for personal email, web browsing, Facebook, or any activity that’s not related to the class. Please try to bring a laptop to class.



Your attendance in class is crucial, as is your punctuality. We are all going to learn this material together, so we need to have everyone present and working. I will make accommodations for an unavoidable absence if you notify me. One necessary absence during the semester is not unusual; having more than two is uncommon.


Much of this course will operate on a collaborative basis, and you are expected and encouraged to work together with a partner or in small groups to study/read, complete in-class lab assignments, and your projects. However, every word that you write must be your own. Copying and pasting sentences, paragraphs, or blocks of code from another student is not acceptable and will receive no credit. All students, staff and faculty are bound by the Smith College Honor Code, which Smith has had since 1944.

Classroom Environment

Realizing the benefits of a diverse space can only occur if we create a climate of psychological safety (Edmondson, 1999). To this end, we will always be respectful of one another. Together we should have the goal of creating an environment where we all feel comfortable sharing our thoughts and opinions. To this end, I value “half-formed,” informal thoughts. Sometimes a deeper understanding is reached via communicating ideas before they are perfectly polished.

Please let me know on the course questionnaire your gender pronoun. In your written work for this class I am fine with (even encourage) the use of “they,” “their,” or simply “she” instead of “his or her” or “he or she.” I am also fine with “ze” and “zir.” Just please do not write “he,” “his” or “himself” when referring to all people. We also should also not say “you guys” when referring to a mixed-gender group, or refer to women as “girls.”

Academic Honor Code Statement

Smith College expects all students to be honest and committed to the principles of academic and intellectual integrity in their preparation and submission of course work and examinations. Students and faculty at Smith are part of an academic community defined by its commitment to scholarship, which depends on scrupulous and attentive acknowledgement of all sources of information, and honest and respectful use of college resources.

Cases of dishonesty, plagiarism, etc., will be reported to the Academic Honor Board.


Everyone should have all that they need to succeed in this course. Bring me your accommodation letter, or have the Disability Office work with me. If you need to register for accommodations, please contact the Disability Services office at ODS@smith.edu. Please check out the office website for more information.


  1. Show-N-tell [10%]: Exposure to many different structural equation models will help you learn to recognize and evaluate these types of models. We can collaborate on bringing in a BUNCH of examples to class. You will find a published peer-reviewed research article that uses structural equation modeling and share it with the class–a show and tell! Your presentation will be about 5 minutes long, walking the class through a diagram of the model tested in the paper. You can draw it on the board, create a slide, or simply pull the paper up on the projector. What did they find? Did they say it was a good fitting model? Did they test alternative models? A few days before you present, email me your article so that I can put it on Moodle for everyone. You are encouraged to share it with me earlier, especially if you are unsure if a particular article is suitable.

  2. In-class Labs [30%]: To build proficiency and experience with actually fitting SEM models in R, we will devote about 35~40% of the in-class time to labs. Labs provide the opportunity to delve into real data sets and build your computational and analytical skills. All labs will use the statistical programming language R and the lavaan package. Lab reports will be written in R Markdown and the resulting HTML files will be submitted via Moodle, generally due on Fridays at 5pm but I expect that you can (hopefully) finish in class.

Over the course of the semester, you will complete a research project in pairs (or individually if you’d prefer–although this is more work for you!). Rather than collect primary data, you will use data available on the Internet or from faculty research (as around). You will present your results in a final report and poster presentation, and complete drafts of the peices of your project thorughout.The project will give you experience planning a statistical study, acquiring data, creating and testing a structural equation model, and writing a technical report. We’ll talk a lot more about the project as the semester proceeds. The peices of the project below are all opportunities for you to draft parts of your final technical report. One document is turned in for your project group/pair.

  1. Initial Project Proposal [5%]: You will prepare a project proposal describing your study, your working model, and obtain approval from your instructor before you begin the investigation. Expect that you will read about 2 to 3 research articles relevant to your dataset domain. In order to specify sound SEMs, you need to know something about the hypothesized causal process behind your variables. In this proposal you will include a working model diagram.

  2. Method Section Draft [10%]: The method section draft will contain everything about your data processing leading up to the final fitting and testing of your SEM. This might include, but is not limited to, how that data was obtained, information about the scales of measured variables and the indicators of latent variables, the reliability of scale scores for path analyses, the choices made in handling of missing data, screening for multivariate outliers, basic information about your sample including demographics for human subjects, etc.

  3. Results Section Draft [10%]: The results section draft will report estimates from your SEM, model fit, any model re-specification, and alternative models.

  4. Poster and Presentation [10%]: During the last week of class, you (and your partner) will create a poster and we will have a poster session.

  5. Technical Report [15%]: The final technical report will include revisions of the initial proposal, method section, and results section. You will also add an abstract and discussion section that relates back to your problem under investigation.

  1. Participation [10%]: Active participation in class and regular attendance will comprise the remainder of your grade.

  2. Extra Credit [?]: Extra credit is available in several ways: attending an out-of-class lectures (as will be announced) and writing a short review of it on Slack; The extra credit is applied when a student is near the boundary of a letter grade.


When grading your written work, I am looking for solutions that are technically correct and reasoning that is clearly explained. Numerically correct answers, alone, are not sufficient on labs, assignments or in the technical report. Neatness and organization are valued, with brief, clear answers that explain your thinking. If I cannot read or follow your work, I cannot give you full credit for it.

Your ability to communicate results, which may be technical in nature, to your audience, which is likely to be non-technical, is critical to your success as a data analyst. The assignments in this class will place an emphasis on the clarity of your writing.

Final Grade Brackets

Grade Percent
A 95-100%
A- 90-95%
B+ 87-89%
B 83-86%
B- 80-82%
C+ 77-79%
C 73-76%
C- 70-72%
D+ 60-66%
D 67-69%
E 59% and below


Course Website and Moodle

The course website will be regularly updated with handouts, project information, labs, and other course resources. Lab assignments, project assignments, and grades will be submitted via Moodle. You should check both regularly.


The use of the R statistical computing environment with the RStudio interface is thoroughly integrated into the course. You have two options for using RStudio:

  • The server version of RStudio on the web. The advantage of using the server version is that all of your work will be stored in the cloud, where it is automatically saved and backed up. This means that you can access your work from any computer with a web browser and an Internet connection.
  • A desktop version of RStudio installed on your machine. The downside to this approach is that your work is only stored locally, and you will have to manage your own installation.

Note that you do not have to choose one or the other – you may use both. However, it is important that you understand the distinction so that you can keep track of your work. Both R and RStudio are free and open-source, and are installed on most computer labs on campus. Please see the Resources page for help with R. Unless otherwise noted, you should assume that it will be helpful to bring a laptop to class, especially on Wednesdays.

Extra Help

There are Statistics TAs available from 7:00-9:00pm on Sunday–Thursday evenings in SR 301 (basement level). They would be great for helping you clean your data prior to fitting your models. In addition, the Spinelli Center for Quantitative Learning (Seeley Hall) supports students doing quantitative work across the curriculum, and has a Data Research and Statistics Counselor available for appointments. Your fellow students are also an excellent source for explanations, tips, etc.

Tentative Schedule

The following is a brief outline of the course. Please refer to the complete day-to-day schedule for more detailed information.

Week Reading Topic
1 Ch. 2 Introduction to SEM; regression review
2 Ch. 4 Psychometrics; data preparation
3 Ch. 6 Path analysis
4 Ch. 8 Causal inference and SEM
5 Ch. 9 & 13 Factor Analysis
6 Ch. 10 & 14 Structural Regression Models
7 Sring Break
8 Ch. 11 & 12 Model fit and estimation
9 Ch. 15 Latent growth modeling
10 Ch. 16 Measurement invairance testing
11 TBD Catch-up week
12 Projects
13 Projects
5/2 Project Presentations
5/9 All work due