If you would like more practice at Exploratory factor analysis (assuming you've already completed the main tutorial exercises), then several further exercises are provided below.

## Teaching quality (Francis 6.1)

### Factor analysis

• student.sav | student.sps | student.spo
• Conduct an EFA of Maths 1 to 10, English 1 to 8, and Sociability 1 to 4 pp. 167-168 (5th ed.)
• Solution (not in Francis): 3 factor (Maths, English and Sociability) PC, varimax, with engl3, engl4, maths3 removed.

## Resilience Scale

### Factor Analysis

• What is the factor structure of the Resilience Scale?
• The designers of the 25-item Resilience Scale (Wagnild & Young. 1993) purported five factors.
• A subset of 15 of the original items is provided from data collected from young Australian adults by Neill & Dias (2001)
• Check whether a five factor solution holds up for the data.
• For this factor analysis, we are interested in developing a theoretical understanding of the underlying psychological components of resilience, so use Principal Axis Factoring (PAF), which looks at the shared variance amongst the items, not all the items' variance.
• You should find that there are really not enough primary loadings on 4 or 5 factors to justify their presence, therefore try 2 and 3 factors.  Best approach is probably 2 factors ("taking control" and "taking it easy"), with 3 to 5 items removed (at least remove the three worst items 2, 8, and 17) and using an oblimin rotation.
• It seems that according to this data, psychological resilience consists of two main underlying components.  The first factor, "Solve" is about taking control, making plans, being determined, task oriented, active, and disciplined, and solving problems (7 items - 1, 14, 10, 15, 6, 24, 21).  The second factor, "Flow" is about a flexible approach to coping, including being able to take things in one's stride, taking it easy, laughing things off, and finding alternative ways through problems (5 items - 19, 7, 23, 16, 9).  People who exhibit both these qualities are people who are most likely to "psychologically resilient" to negative consequences of experiencing risk factors.

### Internal consistency

• What is the internal consistency for each factor?
• Both factors have very good internal consistency (a >.8)

### Composite Scores

• Calculate unit-weighted composite scores for SOLVE and FLOW and create univariate descriptives and histograms.
• Both factors have reasonably normal distributions with some negative skew.
• Get descriptive statistics and histograms to examine each of the distributional properties of the composite scores you've created.
• Compare with descriptives statistics and histograms for the individual items - what are the differences? (The composite score should be more normally distributed)

## Self Description Questionnaire - II

• sdq.sav | sdq.sps | sdq.spo
• (from Neill, 1994)
• The designer of the Self Description Questionnaire - II, a self-concept questionnaire, for adolescents (SDQ-II), Prof. Herb Marsh, proposes 11 factors.  This is a sample of data pertaining to 7 of those factors, collected from Australian adolescents.  Check to see whether there are 7 factors.  Use Principle Components (assume we are doing this in order to calculate factor scores for each self-concept factor).
• Check the scree plot - it will suggest looking at 3, 5 and 8 factors.  Yet, further exploration of the factor loadings suggests that 6 or 7 factors make more sense.  However, there are some cross-loadings between the Opposite-Sex Relations and Physical Appearance items.  These can be minimised by using an oblimin rotation.  A 7 factor solution makes most sense.  Note that if 6 factors are used, that it seems that Opposite-Sex Relations join in one factor with Physical Appearance.  Whilst understandably related, it would make more sense to keep Physical Appearance and Opposite Sex Relations as a separate factors.
• It is also important to test for structural invariance across cohorts within the sample. Further checking of the SDQ data 6 and 7 factor solutions should take place across Gender.  If the factor analyses are done separately by Gender, it becomes apparent that the 6 factor solution can apply to both genders, whereas the 7 factor solution seems to only apply to one gender.  Thus, this is an issue which require further thinking and investigation before ultimately deciding on the most appropriate factor structure.

## Life Effectiveness Questionnaire - H

• leq.sav | leq.sps | leq.spo
• The data is from Neill, Marsh & Richards, 2003
• This file contains data for all 24 items in the Life Effectiveness Questionnaire version H.
• How many factors are evident in this data set?
• Check the screeplot - it will suggest some possibilities. Use Principal Components, since we probably want to create composite scores for use in further analysis.
• An 8 factor solution works well. Oblimin and Varimax solutions are both good, although Oblimin is a bit cleaner. This is a pretty clear solution reflecting the fact that this instrument has been carefully revised through several iterations, each with hundreds or thousands of participants.
• It is important to test for structural invariance across cohorts within the sample. Using the LEQ data, conduct your factor analysis separately for males and females.  Is life effectiveness structured similarly for males and females?
• The number and meaning of the factors for males and females looks similar although the order of the factors suggests a gender-specific emphasis about which factors are most dominant.
• Does the LEQ factor structure also hold up across participant age?
• Recode age into a dichotomous variable for 25 years and below as "young", and 26 years and over as "old".  Split the data file by the new age category variable and conduct the factor analysis with each cohort.  The conclusion would be similar - still the same eight meaningful factors, but there is an age-specific emphasis on which factors are the most dominant.