Latent Trait Measurement and Structural Equation Modeling, Spring 2013 (UNL)

Upcoming Workshops:

Thank you for visiting my course notes. Here are some upcoming opportunities to learn from me and my colleagues in person:

Diagnostic MeasurementMay 22-25, 2017Omni Hilton Head Oceanfront Resort, Hilton Head Island, South CarolinaJonathan Templin
Introduction to Longitudinal Multilevel ModelsMay 30-June 2, 2017Omni Hilton Head Oceanfront Resort, Hilton Head Island, South CarolinaLesa Hoffman

Latent Trait Measurement and Structural Equation Models; Spring 2013, University of Nebraska-Lincoln

External Links:

Instructor: Dr. Jonathan Templin
Phone: (402) 472-7806
Office: 220 Burnett Hall
Office Hours: W 10am-12pm or by appointment
Syllabus: Printable Course Syllabus (last updated 01/05/13)
Communication: Course Facebook Page
Mplus on HCC: Instructions for Accessing Mplus
Video: How to request an HCC account
Video: How to connect to Tusker
Video: How to use Tusker with SSH
Document: How to use Mplus on Tusker

Tentative Schedule of Events:

Links under topics below are .pdf files for the lecture materials.
Media links are .mp4 files recorded from the class lecture (right-click, use save target/link as).



Course Materials


1 1/9 Course Introduction
Review of Matrix Algebra/Multivariate Normal Distribution
Introduction to Mplus

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Homework #1: Due Wednesday, January 16th at 11:59pm
Homework Data File

Kline: Ch. 1
J & W: Chs. 2, 4
2 1/16 Maximum Likelihood
Robust Maximum Likelihood

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Homework #2: Due Wednesday, January 23rd at 11:59pm
Homework Data File

Enders: Chs. 3, 5
3 1/23 Path Analysis (Part 1)

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2

No homework assigned

Kline: Ch. 5
Pajares & Miller (1994)
4 1/30 Path Analysis (Part 2)

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Bonus Non-Homework Assignment (pick one for 1% of your course grade if completed correctly):

  • Recreate the model with two DVs from homework #8 in PSYC 943 ( click here) using Mplus. Submit your Mplus syntax in dropbox. If you were not part of PSYC 943, email me for a log in name and password.
  • Simulate the data from the path analysis reported in Pajares and Miller (1994). Use whatever program you would like. Submit your syntax or program in dropbox.
Kline: Ch. 6
5 2/6 Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Homework #3: Due Wednesday, February 13th at 11:59pm
Homework Data File

6 2/13 Introduction to Confirmatory Factor AnalysisLecture Slides

Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Confirmatory Factor Analysis (CFA): Concepts/Identification/Model Fit
Lecture Slides
Mplus Examples

Lecture Video Part 1

Homework #4: Due Wednesday, February 20th at 11:59pm

R & M: Chs. 6, 7
Brown: Chs. 3, 4, 5
Hu & Bentler (1999)
7 2/20 Introduction to CFA
Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3
Kaplan: Ch. 3
Brown: Ch. 8
8 2/27 Building a Scale with CFA
Lecture Slides

Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2

Homework data file available in Readings folder on Dropbox.

9 3/6 Comparing Classicial Test Theory with CFA
How to use Scores in Secondary Analyses

Lecture Slides

Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Homework #6: Due Wednesday, March 27th at 11:59pm
Homework data file available in Readings folder on Dropbox.

10 3/13 Multifactor Confirmatory Factor Analysis

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

11 3/27 Exploratory Factor Analysis (and Principal Components Analysis)
Conducting Exploratory Analyses with CFA

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

Homework #7: Due Wednesday, April 10th at 11:59pm

Homework data file

J & W: Chs. 8, 9
12 4/3 Structural Equation Modeling: Path Analysis with Latent Variables (part 1)

Lecture Slides
Mplus Example Files

R & M: Ch. 5
Kline: Ch. 8
McDonald & Ho (2002)
13 4/10 Structural Equation Modeling: Path Analysis with Latent Variables (part 2)

Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2

DeShon (1998)
Boomsma (2000)
R & M: Ch. 1
14 4/17 SEM for Non-Normal Outcomes

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2

Kline: Ch. 11
Brown: Ch. 7
Kaplan: Ch. 4
15 4/24 Multiple Group Analyses and Factorial Invariance

Lecture Slides
Mplus Example Files

Lecture Video Part 1
Lecture Video Part 2
Lecture Video Part 3

PSYC 948, Latent Trait Measurement and Structural Equation Models, is a course about the fundamentals of latent variable modeling, path analysis, and structural equation modeling, combining theoretical and practical perspectives. The course is designed to provide details of structural equation modeling, from the statistical underpinnings to how to run many various types of structural equation analyses.

Course Objectives

Overall, this course is a course that teaches multivariate statistical thinking, structural equation modeling, and the language of both methods. By the end of the course, students are expected to:

  • Understand the types of hypotheses and research questions for which structural equation modeling is used
  • Know and perform structural equation modeling techniques using Mplus
  • Understand how structural equation models fit into a larger framework of statistical methods

Be advised: this course will challenge you, and will require a significant commitment, both in amount of time and in amount of work. Expect to spend 9 – 12 hours outside of class each week on this course. Reading the assigned papers and chapters in advance of lecture, completing the homework each week, and attending class are keys to your success.

Required Textbook

None- Readings will be assigned and administered via Dropbox each week.


This course assumes you have taken multivariate statistics coursework. Within the Department of Psychology at the University of Nebraska-Lincoln, this means having taken and completed PSYC 943. The first homework (assigned the first day of class and due next Wednesday) is designed to test your knowledge of the prerequisites.

Statistical Computing

This course will use Mplus for all statistical analyses. Mplus, a powerful generalized modeling package, is available to you in two ways:

  1. You can purchase your own copy of Mplus through the Muthen & Muthen website: (easy but expensive)
  2. You can sign up to use Mplus through the Holland Computing Center using secure shell terminal connections (technical and frustrating, but free – see the first lecture)

Because of new software licensing policies at UNL, Mplus will likely be unavailable through the Burnett computer labs. Please be advised as each homework assignment will require the use of Mplus.

Academic Honesty:

As a reminder, the University has a policy on academic honesty (see the Graduate Studies Bulletin).
All course assignments should be done individually.

Accommodating Persons with Disabilities:

Students with disabilities are encouraged to contact the instructor for a confidential discussion
of their individual needs for academic accommodation. It is the policy of UNL to provide flexible and
individualized accommodation to students with documented disabilities that may affect their ability
to fully participate in course activities or to meet course requirements. To receive accommodation
services, students must be registered with the Services for Students with Disabilities (SSD) office,
132 Canfield Administration, 472-3787 voice or TTY.

Course Website/Technology

This course will not use Blackboard. Instead, we will use freely available commercial software for communication and dissemination of course materials.

Audio/Video Recordings of Class

I will be making a flash recording of each class, which will be posted on the website by the end of the day following class.

Class Page on Facebook

In order to facilitate communication, I have created a Facebook page where I will:

  1. Post information about the course
  2. Hold online office hours (as needed)
  3. Answer your questions directly using the wall feature

The Facebook page is designed to facilitate discussion in a manner that is easily accessible by all students and auditors of the course. To be a part of the discussion, please search for PSYC 948. To follow, you must “like” the page.

Course Materials Over Dropbox

All course readings will be available over a shared folder on Dropbox, a file repository online ( To gain access to the shared folder, please send me an email. You do not have to install the Dropbox application as you can download files from any web browser.

If you do not have a Dropbox account, please email me for an invitation.

Course Website

Course lecture slides, lecture examples, flash video files, assignments, and information are available on the website.

Course Requirements:

Student evaluation will be made on the basis of homework grades. All homework and answers must be your own and not be copied or paraphrased from anyone else’s answers. You are
responsible for your own work.

Homework Assignments:

Homework assignments will be administered in order to give students practice applying techniques discussed in class and will be due at the start of class the following week. Each assignment must be at least 75% complete in order to be accepted for grading. Homework must be submitted electronically (email in the form of Microsoft Word document with the name: 948_FirstLast_HW#.docx.

Do not wait until the last minute to do your homework.

Note: Each homework assignment will have a section where you can perform similar analyses on data that is your own. If you do not have your own data set, please contact me to obtain one to use throughout the semester.

Policy on Late Homework Assignments:

Late homework will have a penalty of 10% of the total per calendar day (any homework later than 10 days late will not be accepted). Resubmission of late homework is allowed, but the maximum grade cannot exceed the maximum amount allowed by the late penalty.

Policy on Late Take-Home Final Exams:

In order to give participants as much time as is possible to work on the final exam, the due date for submitting
the completed final exam falls shortly before course grades are due. Therefore, late final drafts will not be accepted.
Participants are not required to submit first drafts of the final exam, but are strongly encouraged to do so,
as the take-home final exam factors heavily into the overall course grade.

Final grades will be determined according to the proportion earned of 100 possible points:

=97 = A+ 93-96 = A 90–92 = A- 87-89 = B+ 83-86 = B 80-82 = B- < 80 = see syllabus

Policy on Assigning Incompletes:

A grade of “incomplete” will be assigned ONLY in the case of extenuating circumstances that
prevent participants from completing course requirements in a timely manner.

Course Style and Content

Lecture Format

Most lectures will have notes (slides) available digitally, with slides available online by the morning of the day of the lecture. Please check the course website before coming to class if you would like to bring a printout of the slides with you. If nothing is posted, then we will be having lecture without slides. I strongly encourage you to participate in lecture by asking questions whenever anything is unclear.

Reading Assignments

To be fully successful in this course, I strongly encourage you to read the assigned papers and/or chapter(s) prior to the coming to class when we will cover the topic. Even if you have difficulty reading the material, exposure to the information prior to lecture will aid in your understanding of the course. Remember, this course is about learning the language of structural equation modeling and multivariate statistics – something that takes immersion in the readings.

How to Succeed in this Course

  • Read the assigned papers (even if it doesn’t make sense to you – it will eventually)
  • Come to class (and bring your questions about what you just read that week)
  • Ask questions when you do not understand
  • Come to office hours
  • Do the homework (consider it practice on applying statistics)
  • Compare your homework with the solutions online before receiving your feedback

All readings will be available online through Blackboard
Readings will be added throughout the semester, but below is the current list.

Book Chapters:

Brown, T. A. (2006). Confirmatory factor analysis for applied research.
New York: Guilford.

Embretson, S. E. & Reise, S. P. (2000). Item Response Theory for Psychologists.
Mahwah, NJ: Erlbaum.

Enders, C. K. (2010).
Applied missing data analysis.
New York, NY: Guilford.

Johnson, R. A. & Wichern, D. W. (2002).
Applied multivariate statistical analysis
(5th Ed.).
Upper Saddle River, N.J.: Prentice-Hall.

Kaplan, D. (2009). Structural equation modeling: foundations and extensions (2nd Ed.). Thousand Oaks, CA: Sage.

Kline, R. B. (2002). Principles and practice of structural equation modeling (2nd Ed.). New York, NY: Guilford.

Raykov, R. & Marcoulides, G. A. (2011). Introduction to psychometric theory. New York: Routledge.

Rupp, A. A, Templin, J., Henson, R. A. (2010). Diagnostic measurement: Theory, Methods, and Applications. New York: Guilford.

Journal Articles:

Atkins, D. C., & Gallop, R. J. (2007). Rethinking how family researchers model infrequent outcomes: A tutorial on count regression and zero-inflated models.
Journal of Family Psychology, 21, 726-735.

Bauer, D. J., & Hussong, A. M. (2009). Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models. Psychological Methods, 14, 101-125.

Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7, 461-483.

DeShon, R. P. (1998). A cautionary note on measurement error corrections in structural equation models. Psychological Methods, 3, 412-423.

Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.

McDonald, R. P., & Ho, M.-H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.

Parajes, F., & Miller, M. D. (1994). Role ofS self-efficacy ad self-concept beliefs in mathematical problem solving: A path analysis.Journal of Educational Psychology, 86, 193-203.