ESRM 6553: Advanced Multivariate Analysis

Spring 2024, Mondays, 5:00-7:45PM, Classroom GRAD 0229


Jihong Zhang


January 13, 2024


February 7, 2024

1 General Information

  • Course Code: ESRM 6553
  • Course ID: 026376
  • Course time and location: Mon 17:00-19:45; GRAD 229
  • Instructor: Jihong Zhang
  • Contact Information:
  • Personal Website:
  • Office Location: GRAD 0109
  • Office Hours: Tu 1:30-4:30PM
  • Office Phone +1 479-575-5235
  • Classroom: GRAD 229
  • Semester: Spring 2024
  • Credits: 3 credit hours

1.1 Course Topics

  1. Introduction to Bayesian Statistics
    • Bayes Theorem;
    • Probability distributions, such as likelihood, priors and posteriors;
    • Theoretical foundations of Bayesian inference;
  2. Bayesian analysis in Stan
    • Basic Stan coding;
    • R package cmdstanr ;
    • Efficient programming using vectorization;
  3. Bayesian Inference and Computational Methods
    • Markov Chain Monte Carlo (MCMC) estimation procedures, such as Gibbs/Hamiltonian sampling;
    • MCMC sampling settings, such as burnins, warmups, and MCMC chains;
  4. Bayesian Modeling Evaluation
    • Model specification, estimation, and testing;
    • Model fit and model comparison, such as convergence diagnostics, posterior predictive checks, information criteria;
  5. Bayesian Modeling
    • Estimating and making inferences from psychometric models such as Confirmatory Factor Analysis (CFA) or Item Response Theory (IRT) models;
  6. Advanced Topics in Bayesian Multivariate Analysis
    • Bayesian networks;
    • Multilevel/Hierarchical models, mixture models;
    • Missing data, non-normal data;

1.2 Course Description

This course offers an in-depth exploration of multivariate statistics within the context of Bayesian inferences. Bayesian statistics have been widely used in public health, education, and psychology. Bayesian techniques are increasingly used in Artificial Intelligence and Brain models for decision-making under uncertainty. Designed for graduate students in educational statistics and research methods, it focuses on the theoretical underpinnings and practical applications of Bayesian approaches in psychometric modeling. Prerequisites include basic knowledge of multivariate statistics and psychometrics.

1.3 Course Objectives

Upon completion of ESRM 6554 - Adv. Multivariate, students will:

  1. Comprehend fundamental concepts and principles of Bayesian multivariate analysis;
  2. Articulate the rationale of Bayesian approaches to data analysis and statistical inference;
  3. Compare Bayesian inference to MLE;
  4. Develop conceptual and mathematical Bayesian literacy, as well as computer software skills (e.g., R, Stan, or JAGS) required to conduct Bayesian data analyses in educational research;
  5. Gain technical foundations necessary to be contributors to applied and methodological research that use Bayesian methods;
  6. Conduct analyses on empirical data, interpret results, and communicate work in written and oral presentations.

1.4 Prerequisite Knowledge

It is assumed that students have has solid statistical training up to and including topics in multivariate statistics (ESRM 6413, 6423, and 6453). In addition, it is assumed you are familiar with R programming (python or SAS are fine). SPSS may not be sufficient for this course.

  • Lectures for theoretical understanding.
  • Hands-on sessions with statistical software.
  • Group discussions and presentations.
  • Research project guidance.

1.5 How to Be Successful in This Class

  • Come to class ready to learn.
  • Complete the out-of-class exercises prior to each class.
  • If you become confused or don’t fully grasp a concept, ask for help from your instructor
  • Know what is going on: keep up with email, course announcements, and the course schedule.
  • Try to apply the information to your area of interest — if you have a cool research idea, come talk to me!

2 Course Materials

2.1 Required Materials

2.2 Optional Materials

2.3 Software

  • R and R packages (tidyverse)
  • Stan is gaining in popularity and has an avid user community. To use Stan in R, you need to download RStan or cmdstanr package. Here is the tutorial of installing RStan or click here for installing cmdstanr package.
  • (Optional) Mplus, JAGS, WinBUGS

3 Assignments

3.1 Online Homework

Online Homework Portal

3.2 Projects

Students will complete a project utilizing your knowledge learnt from the class. You may work individually. I will provide data and questions for this project OR you can use data that is of interest to you in your GA position or dissertation research. The primary objective of the research project is to facilitate the application and understanding of concepts learned in this course.

There will be a short project proposal due around week 15 - it can be sooner if you want to get started early. Required for this proposal is an NCME-type conference proposal (800 words maximum). Please see Individual Paper Presentations for more details

Typical components of the research proposal include:

  • Title (no more than 12 words)
  • Summary of research (no more than 800 words)
    • Background of research
    • Research questions/hypotheses
    • Method (Data, Analysis Plan)
    • Preliminary findings
    • References/Table/Figure

3.3 In-Class Short Quiz

At the commencement of each class session, a brief quiz consisting of one to three questions will be administered. These quizzes are intended for formative assessment purposes only and will not contribute to your overall score. However, regular attendance is essential, as it will ensure full credit in the final grading process.

3.4 Grading

  1. Brief quiz: 60%
  2. Project Presentation: 20%
  3. Project Proposal: 20%

4 Academic Policies

4.1 AI Statement

Specific permissions will be provided to students regarding the use of generative artificial intelligence tools on certain graded activities in this course. In these instances, I will communicate explicit permission as well as expectations and any pertinent limitations for use and attribution. Without this permission, the use of generative artificial intelligence tools in any capacity while completing academic work submitted for credit, independently or collaboratively, will be considered academic dishonesty and reported to the Office of Academic Initiatives and Integrity.

4.2 Academic Integrity

You are responsible for reading and understanding the University of Arkansas’ Academic Integrity Policy. You are expected to complete all assignments and exams with the highest level of integrity. Any form of academic dishonesty will result in a failing grade for the course and will be reported to the Office of Academic Integrity. If you have any questions about what constitutes academic dishonesty, please ask me.

4.3 Emergency Preparedness

The University of Arkansas is committed to providing a safe and healthy environment for study and work. In that regard, the university has developed a campus safety plan and an emergency preparedness plan to respond to a variety of emergency situations. The emergency preparedness plan can be found at Additionally, the university uses a campus-wide emergency notification system, UARKAlert, to communicate important emergency information via email and text messaging. To learn more and to sign up:

4.4 Inclement Weather

Each faculty member is responsible for determining whether or not to cancel class due to inclement weather. If you have any questions about whether or not class will be held, please contact me. If I cancel class, I will notify you via email and/or Blackboard. In general, students need to know how and when they will be notified in the event that class is cancelled for weather-related reasons. Please see here for more information.

4.5 Academic Support

A complete list and brief description of academic support programs can be found on the University’s Academic Support site, along with links to the specific services, hours, and locations. Faculty are encouraged to be familiar with these programs and to assist students with finding an using the support services that will help them be successful. Please see here for more information.

4.6 Religious Holidays

The university does not observe religious holidays; however Campus Council has passed the following resolution concerning individual observance of religious holidays and class attendance:

When members of any religion seek to be excused from class for religious reasons, they are expected to provide their instructors with a schedule of religious holidays that they intend to observe, in writing, before the completion of the first week of classes.

5 Schedule

Weekly breakdown of topics and readings:

Week Date Topic Reading Topic Slides Code/Data
1 01/15 No Class
2 01/22 Introduction to Bayesian Statistics Part I SR1 Chapter 1; BDA2 Chapter 1 (Optional) Course and Bayesian Analysis Introduction Lecture01_Jan22
3 01/29 Introduction to Bayesian Statistics Part II SR Chapter 2 Introduction to Bayesian Concepts Lecture02_Jan29
4 02/05 Bayesian Inference and Computational Methods I SR Chapter 9 Linear Regression Model with Stan Lecture03_Feb05
  1. DietGroup.csv
  2. DietDataExample.R
  3. EmptyModel.stan
  4. EmptyModelPoor.stan
5 02/12 Bayesian Inference and Computational Methods II StanUserGuide:Chapter21 Linear Regression Model with Stan II



  1. DietDataExample2.R
  2. FullModel_Old.stan
  3. FullModel_New.stan
  4. FullModel_compute.stan
  5. FullModel_contrast.stan
6 02/19 Bayesian Inference and Computational Methods III SR Chapter 9.2 & 9.3 Bayesian Model Fit and Comparisons Lecture05_Feb19
  1. Lecture05.R
  2. FullModel_PPP.stan
7 02/26 Bayesian Modeling Evaluation I: Model diagnosis SR Chapter 7.1 & BPM3 Chapter 10
8 03/04 Bayesian Modeling Evaluation II SR Chapter 7.4 & 7.5
9 03/11 Bayesian Modeling I: CFA BPM Chapter 9
10 03/18 Spring Break
11 03/25 Bayesian Modeling II: IRT BPM Chapter 11
12 04/01 Bayesian Modeling III: CDM BPM Chapter 13
13 04/08 Advanced Topics I: Non-normal data
14 04/15 Advanced Topics II: Multilevel SR Chapter 11
15 04/22 Advanced Topics III: Missing Data, Measurement Error SR Chapter 15
16 04/29 Student Presentations

Academic calendar for Spring 2024: Here

6 Other Online Materials

6.1 Applied Statistics

  1. Bayesian Data Analysis, by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin.

6.2 Cognitive Science

  1. An Introduction to Bayesian Data Analysis for Cognitive Science, by Bruno Nicenboim, Daniel Schad, and Shravan Vasishth)
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  1. SR: Statistical Rethinking 2ed Edition by Richard McElreath↩︎

  2. BDA: Bayesian Data Analysis by Gelman et al. (2021)↩︎

  3. BPM: Bayesian Psychometric Modeling by Levy, Mislevy (2016)↩︎