Psychology 405: Psychometric Theory
William Revelle
Swift 315
email: revelle@northwestern.edu
May 28, 2024

1

Outline (to be added to frequently – keep checking)This is the abbreviated form of the syllabus, The full syllabus is at https://personality-project.org/courses/405/405.syllabus.pd
Current version of May 28, 2024

1.1News of changes

Will appear here when I make them.
April 10: Updated the More on correlations slides.
May 15: Updated the sem vs. cfa slides. Updated psych Current date is packageDate(”psych”) [1] ”202405-14”
May 28: Updated psych Current date is packageDate(”psych”) ”2024-05-26” Note that this is version 2.4.5
and needs to be downloaded from the personality server to work.
The review session on Wednesday will be held by zoom at 847-491-7700,

11.2

Assignments as a table

Week
1a

Topic
Correlational and Experimental Psychology

1b2aModels of Measurement

2b

Variance and Covariance

3aVariance and Covariance3b4aLatent variable models

4b5aMidterm

5b

ReliabilityLecture Notes
Overview
Theory of Data
Metric properties andthe problems of scaleCorrelation and Regression (Part 1)

Correlation and Regression (Part2)
Linear algebra
More on correlations andregression
Factor Analysis

Even more fa
Reliability Theory

6a

Item Response Theory

Item Response Theory

6bValidity

7

Scale Construction

Validity
Validityof
SAPA methods
Validity- another lookscale construction

8

Confirmatory analysis
StructuralEquation
Modeling

9

Other approaches

efa vs. cfa
sem vs. cfa continued
Goodness of fit
Further topics
Review of 405

Readings
Chapter 1: the role of measurement
Chapter 2: Theory of Data
Chapter 3: The problems ofscale
Chapter 4: Correlation
Francis Galton & Charles
Spearman
Review of linear/matrix algebra (Appendix E)
Multiple
Correlations(Chapter 5)Constructs,Components,and Factors (Chapter 6)
latent variables = Easter
Bunnies?
Reliability (Chapter 7)
α to ω
Supplement to α to ω
Item
ResponseTheory(Chapter 8)
Predicting the Persome
That takes the BISCUIT
fishing nets
Fishing Spears and FishingNets
more on validity
sem chapters 3, 4,

Homework/ R help
Getting started with R
Appendix A: Using R
Homework #1 with answers
Using R for statistics and aneven shorter guide to R
Simple Regression problems#2
More problems

Applications of correlations
Problem set 3
Factor Analysis (How To)
Homework set 4
sample questions

Omega Analysis (How To)
Homework set 5
Problems
Factor approaches to IRT seesection 7 Homework set 6

scoring scales
Homework set 7
Factor analysis and sem

5, 6
Final ProjectThis table and the entire syllabus is being converted from HTML to LAT X. The original version is here
E2

Detailed Notes

2.1

Week 1Introduction to latent variables (405 in a week).
Review of Correlation and Regression and classical reliability theory (Revelle and Condon, 2018a,b). See also
Chapter 4 on Correlation and regression as well as Chapter 5 on multiple correlation and regression.
Review of linear/matrix algebra (Appendix E)
What is a latent variable? Some opposing viewpoints (Bartholomew et al., 2009; Loevinger, 1957; Markonand Jonas, 2016; Jonas and Markon, 2016)

2.2

Week 2

Application of matrix algebra to pattern and structure. Chapter 6: Exploratory factor analysis as a basic
latent variable model. Finding the inverse of a matrix. For a review of factor analysis, see https://personality-project.org/courses/405/405-efa.pdf.

2.3

Week 3Structural models and goodness of fit tests. Barrett (2007), Examples with simulated data.
How to simulate structural data. This has been revised with a correction for two factor simulations andwith a more extensive analysis of the effects of sample size on estimating parameters in the two factor
model.

2

Using basic sem programs to find structure and apply goodness of fit tests. Using the sem (Fox et al., 2013)and lavaan (Rosseel, 2012) packages.

2.4

Week 4Perhaps the fundamental issue of latent variable analysis is why use latent variables. The classic developmentof latent variable analysis was (Spearman, 1904) with the development of what has come to be called“Exploratory Factor Analysis”. While a useful descriptive technique to describe the “common” part ofvariables, EFA can be made a testable technique using “Confirmatory Factor Analysis” which is the root ofmost SEM packages. See EFA/CFA for an overview of PCA, EFA, and then the basics of CFA. EFA/CFA– psych, sem and lavaan.
The problem of hierarchical representations of data. Many people claim a “general factor” of personality
in analogy to the ‘g’ factor of ability. This has been disputed (Revelle and Wilt, 2013). See also A generalfactor of personality? talk given at an “Experts Meeting” on personality structure. Also see Analysis ofhierarchical factor models using hierarchical and bifactor solutions. The lecture notes for week 4 are here
and prior notes are prior year notes

2.5

Week 5

Exploratory and confirmatory factor analysis, continued. The lecture notes for week 5 are here.
Considering issues of using items rather than continuous measures. items vs continuous measures. Unfortunately, items have serious problems with skew.
One of the most powerful applications of sem is the analysis of change.

2.6

Week 6Comparing three examples from the literature: a short example (Erdle et al., 2009) of how not to reportfactor analysis, a sem paper which which actually fails to identify the model correctly (Erdle et al., 2010) andanother (Marsh et al., 2010) which systematically compares models. This last one includes a good discussionof how to do measurement invariance.

2.7

Week 7

lavaan uses many examples from the MPlus manual (https://www.statmodel.com/ugexcerpts.shtml.
See in particular the example data sets at https://www.statmodel.com/usersguide/chapter5.shtml.
The notes describing lavaan output for these examples are available here.

2.8

Week 8Comparing sem in R and LISREL (Jöreskog and Sörbom, 1999). Consideration of goodness of fit tests(Barratt et al., 2007) (Click on Issue 5 in the left hand column). R and LISREL lecture notes
For a very good discussion of latent change estimation in R see Ghisletta and McArdle,( 2014 ) (Ghislettaand McArdle, 2012). Also see the lecture notes from Yves Rosseel Modeling change with lavaan
For an example of modeling change in cognitive ability and depression to examine the temporal sequencingof the effects, look at Aichele et al. (2018).
An excellent set of lecture notes on testing for invariance comes from Tutorial on measurement invariance
Kate Xu.

2.9

Week 10

Course review

32.10SoftwareCommercial software for structural equation modeling: EQS Bentler (1995), LISREL (Jöreskog and Sörbom,1999) MPlus (Muthén and Muthén, 2007).

2.11R advice

The R tutorial gives a short introduction to the use of R.
• (Macs and PCs) For this, or any other package to work, you must activate it by either using thePackage Manager or the “library” command:– type library(psych)– If loading the psych package works, function such as describe and pairs.panels should work
(or at least give an error message that is NOT “could not find function”).
– entering ?psych will give a list of the functions available in the psych package.

References
Aichele, S., Ghisletta, P., Corley, J., Pattie, A., Taylor, A. M., Starr, J. M., and Deary, I. J. (2018).
Fluid intelligence predicts change in depressive symptoms in later life: The Lothian birth cohort 1936.
Psychological Science, 29(12):1984–1995.
Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42(5):815–824.
Bartholomew, D., Deary, I., and Lawn, M. (2009). A new lease of life for Thomson’s bonds model ofintelligence. Psychological review, 116(3):567–579.
Bentler, P. M. (1995). EQS structural equations program manual. Multivariate Software, Inc., Encino, CA.
Erdle, S., Gosling, S. D., and Potter, J. (2009). Does self-esteem account for the higher-order factors of thebig five? Journal of Research in Personality, 43(5):921 – 922.
Erdle, S., Irwing, P., Rushton, J. P., and Park, J. (2010). The general factor of personality and its relation
to self-esteem in 628,640 internet respondents. Personality and Individual Differences, 48(3):343–346.
Fox, J., Nie, Z., and Byrnes, J. (2013). sem: Structural Equation Models. R package version 3.1-3.
Ghisletta, P. and McArdle, J. J. (2012). Latent curve models and latent change score models estimated in
R. Structural Equation Modeling: A Multidisciplinary Journal, 19(4):651–682. PMID: 25505366.
Jonas, K. G. and Markon, K. E. (2016). A descriptivist approach to trait conceptualization and inference.
Psychological Review., 123(1):90–96.
Jöreskog, K. G. and Sörbom, D. (1999). LISREL 8: Structural equation modeling with the SIMPLIS commandlanguage. Scientific Software International, Lincolnwood.
Loehlin, J. C. and Beaujean, A. (2017). Latent variable models: an introduction to factor, path, and structural
equation analysis. Routledge, Mahwah, N.J., 5th edition.
Loevinger, J. (1957). Objective tests as instruments of psychological theory. Psychological Reports Monograph
Supplement 9, 3:635–694.
Markon, K. E. and Jonas, K. G. (2016). Structure as cause and representation: Implications of descriptivist
inference for structural modeling across multiple levels of analysis. Journal of Abnormal Psychology,
125(8):1146 – 1157.

4

Marsh, H. W., Scalas, L. F., and Nagengast, B. (2010). Longitudinal tests of competing factor structures
for the rosenberg self-esteem scale: Traits, ephemeral artifacts, and stable response styles. Psychological
Assessment, 22(2):366 – 381.
Muthén, L. and Muthén, B. (2007). Mplus User’s Guide. Muthén & Muthén, Los Angeles, CA, fifth edition
edition.
R Core Team (2023). R: A Language and Environment for Statistical Computing. R Foundation for StatisticalComputing, Vienna, Austria.
Raykov, T. and Marcoulides, G. A. (2006). A first course in structural equation modeling. Lawrence Erlbaum
Associates, Mawwah,N.J, 2nd edition.
Revelle, W. (2024). psych:Procedures for Psychological, Psychometric, and Personality Research. Northwestern University, Evanston, https://CRAN.r-project.org/package=psych, 2.4.3 edition. R package version
2.4.3.
Revelle, W. (in prep). An introduction to psychometric theory with applications in R. Springer.
Revelle, W. and Condon, D. M. (2018a). Reliability. In Irwing, P., Booth, T., and Hughes, D. J., editors,
The Wiley Handbook of Psychometric Testing: A Multidisciplinary Reference on Survey, Scale and Test
Development. John Wily & Sons, London.
Revelle, W. and Condon, D. M. (2018b).
https://osf.io/e685p/).

Reliability from α to ω:

A tutorial.

(under review:Revelle, W. and Wilt, J. (2013). The general factor of personality: A general critique. Journal of Research
in Personality, 47(5):493–504.
Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software,48(2):1–36.
Spearman, C. (1904). “General Intelligence,” objectively determined and measured. American Journal of
Psychology, 15(2):201–292.

5