PSYn5440 – Introduction to Factor Analysis
Final Exam, Fall 2021
Due midnight, January 20th, 2022
Read the 1999 paper by Tomas and Oliver on the factor structure of Rosenberg’s Self-Esteem
Scale (RSE; the paper can be found in IS as tomas_oliver1999.pdf). I’ve (among other reasons)
chosen this paper because it’s quite a good (if a bit old) review of things we’ve learned
throughout the semester – and I belive that after all we’ve learned, you should be fairly
comfortable reading papers like this (in journals like Structural Equation Modeling, oh my!).
As it so happens, this website offers a lot of free self-report data to download and study. I’ve
downloaded the data for the RSE, randomly taken two samples of N = 1000 each and calculated
the correlation matrices for the ten RSE items. Find the matrices in IS in .csv files (cormat1.csv,
cormat2.csv), where you can also find the accompanying codebook for the dataset
(codebook.txt).
As you can see from the paper by Tomas and Oliver, different contesting ideas about what the
questionnaire really measures can lead to different model formulations. Take a look at Figure 1
and the nine different path diagrams. Here, we will focus on models 1, 2, and 7 (I will further
refer to them using this original numbering). As in Assignment 2, attach the R script file you
have used for Part 2 to your submitted assignment and, in case you did not use R, attach the
output as well.
Part 1
Using the data in cormat1.csv, I have obtained Ordinary Least Squares solution using CEFA for
m = 1 and m = 2 factors. For the two-factor solution, I have applied an oblique Varimax and
oblique Quartimax rotations. You can find the outputs in Exam_Part1_1f.out,
Exam_Part1_2f_quartimax.out, and Exam_Part1_2f_varimax.out.
a) For the 1-factor model, explain the relationship between the value of the OLS discrepancy
function and the elements in the residual correlation matrix in your own words.
b) If you would fit the 1-factor model using Maximum Likelihood instead, but you would still
compute the RSS measure from the residual matrix, which method – OLS or ML – would
produce a lower RSS value? Explain why.
c) Considering your results, which model from the original paper by Thomas and Oliver would
you lean towards – Model 1, Model 2, or Model 7? Briefly summarize why.
Part 2
Use the correlation matrix in cormat2.csv for this part of the exam. Use R.
Fit the Models 1, 2, and 7 from the paper by Tomas and Oliver. Interpret on the meaning of the
factors in each of the three models. Briefly write up the results (you can get inspiration from
the paper itself, or from the guide I’ve referenced in Assignment 3), but nothing too long,
please. Your write-up should result in a conclusion regarding which model would you choose
and why.