Psychometrics tutorial - Exploratory factor analysis
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This tutorial provides an introduction to conducting exploratory factor analyses (EFAs) using SPSS. The SPSS data, syntax and output is available for each analysis, along with screencasts on youtube.

General steps

Here are the recommended steps when conducting an exploratory factor analysis using SPSS:

1. Get to know the data:
1. Univariate distributions: Explore the distribution and central tendency for each of the variables statistically (e.g., use descriptive statistics to examine the M, SD, skewness, and kurtosis) and graphically (e.g., histograms)).
2. Bivariate distributions: Examine the bivariate correlations statistically (e.g., correlation matrix) and graphically (e.g., scatterplots)
2. Examine EFA assumptions:
1. Sample size
2. Linearity
3. Homoscedasticity
4. Factorability
3. Conduct EFA (repeat until a good model is identified - may require many different analyses involving different numbers of factors, different types of rotation, and different sets of items):
1. Via Pull-down menus: Analyze - Data Reduction - Factor Analysis - Put target variables into the Variables box (order doesn't matter, but the output will be neater to read if the variables are sequentially ordered from 1 to X)
2. Descriptives - check these options:
1. Initial solution
2. Correlation matrix
1. Coefficients
2. KMO and Bartlett's
3. Anti-image
3. Extraction - check these options:
1. Analyse - Correlation matrix
2. Display - Screen plot
3. Extract - Eigenvalues over 1 - or usually better is to specify the number of factors
4. Rotation - Varimax (uncorrelated factors) or Direct Oblimin (correlated factors)
1. Options - check these options:
1. Sorted by size
2. Suppress values less than .20
4. After checking internal consistency and creating composite scores, work out the correlations between the factors: In SPSS - Analyze - Correlate - Bivariate - and put all of the composite factor scores in.
5. Report the factor correlations in the EFA results

Exercises

Exercise 1: Smoking attitudes

What are the underlying dimensions of attitudes towards other people smoking?

 View the accompanying screencasts: [1] [2] [3]

Data file: data_14_1.sav | .sps | .spo
Allen & Bennett Ch 14 (pp. 193-204) [1]

Rating scale
 On a scale from 1 to 100, where 1 represents "strongly disagree" and 100 represents "strongly agree"; please indicate the extent with which you agree with each of the following statements.
Items
 1 I think smoking is acceptable. 2 I don't care if people smoke around me. 3 I don't think people should smoke in restaurants. 4 I think people should have the right to smoke. 5 I don't think people should smoke around food.
Solution
• PAF, Varimax or Oblimin rotation (5 items; N = 107), 2 factors:
1. Smoking acceptance (3 items)
2. Smoking in food/restaurants (2 items)

Exercise 2: Classroom behaviour

 View the accompanying screencasts: [4] [5] [6]

Data file: behav.sav | .sps | .spo | .doc | .pdf
Francis 5.6 (pp. 157-166)[2]

Rating scale (1 to 5)
 Teachers, for each of the following paired behavioral statements, please mark a cross over the dot which is nearest the statement that best describes the TYPICAL behavior of THIS student at school
Items
 1 CONCENTRATES Cannot concentrate on any particular task; easily distracted ↔Can concentrate on any task; not easily distracted 2 CURIOUS Shows little curiousity or motivation ↔Eager to learn; curious and enquiring 3 PERSEVERES Lacks perseverance; is impatient with difficult or challenging work ↔Perseveres in the face of difficult or challenging work 4 EVEN-TEMPERED Irritable,'touchy', 'cranky' ↔Even-tempered 5 PLACID Easily excited; gets 'high' ↔Not easily excited; placid 6 COMPLIANT Demanding and argumentative ↔Patient and compliant 7 SELF-CONTROLLED Has difficulty controlling own behaviour ↔Is able to control own behaviour 8 RELATES-WARMLY Provocative; disruptive; short attention span ↔Relates warmly to others 9 SUSTAINED ATTENTION Easily frustrated; short attention span ↔Persistent, sustained attention span 10 COMMUNICATIVE Difficult to reason and communicate with ↔Easy to reason and communicate with 11 RELAXED Restless; fidgety; can't sit still ↔Relaxed; can sit still 12 CALM On the go; lively; always moving ↔Settled, calm 13 PURPOSEFUL ACTIVITY Aimless activity ↔Purposeful activity 14 COOPERATIVE Disputes, fights over sharing ↔Co-operative; shared with others 15 CONTENTED Is easily upset; unhappy ↔Contented; happy
Solution
• Solution: 3-factor PAF, Oblimin rotation (13 items; N = 1500), Drop items 6 and 7
1. Sociability
3. Settledness
• See also: Lecture slides: 33-36, 38, 40, 42, 52, 54, 56, 58, 78-80

Exercise 3: Managerial skills

 View the accompanying screencast: [7]

Data file: manage.sav | .sps | .spo | .doc | .pdf
Francis 5.12 (pp. 166, 258) [3]

Rating scale
 Try to assess the extent to which you possess these skills (Scores ranged from 1 = very little extent to 7 = to a very great extent.)
Items
 1 I show confidence in my staff 2 I let my staff know they are doing well 3 I give feedback to staff on how well they are working 4 I would personally compliment staff if they did outstanding work 5 I believe in setting goals and achieving them 6 I achieve the things I want to get done in a day 7 I never try to put off until tomorrow what I can finish today 8 I plan the use of my time well 9 I remain clear headed when too many demands are made upon me 10 I rarely overlook important factors when plans are made 11 I handle complex problems efficiently
Solution
• Solution: 3 factor PAF Oblimin (13 items; N = 114):
1. Feedback
2. Time Management
3. Problem Solving