Using Exploratory and Confirmatory Factor Analysis to Understand Social Attitudes

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Using Exploratory and Confirmatory Factor
Analysis to Understand Social Attitudes

• Paula Surridge
• Dept. of Sociology
• University of Bristol
• p.surridge_at_bris.ac.uk

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The project

• The making of social values
• Examine relationship between education, social
  class and social attitudes
• Framework based around idea of underlying values
  which structure social attitudes

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Core values?

• Underlying values that determine how specific
  issues are viewed
• Not directly observable
• Stable and durable over time

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Measuring Core Values

• Socialist Laissez-faire (Left-right)
• Liberal-Authoritarian
• Evans et al 1996
• Heath et al 1994
• Use a combination of attitudinal items to measure
  core values

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Project research questions

• Are the left-right and liberal-authoritarian
  values of British public changing?
• How is this related to increases in educational
  levels, especially higher education?

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Assumptions

• There are two basic values underpinning social
  attitudes
• Invariant in structure over time
• Invariant in structure over groups
• New issues do not disrupt basic structure
• Need to assess if these assumptions reasonable

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Exploratory Factor Analysis

• Key question
• How are new issues related to the two core
  values as measured by left-right and
  liberal-authoritarian scales
• Exploratory analysis no preconceived ideas of how
  issues might be related

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The data

• British social attitudes survey, 2004 2005
• Sample size 2500
• Analysis conducted for 2004, 2005 used for
  validation

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Exploratory Factor Analysis

• Issues
• Suitability of the data
• Sample size
• Number of measures per factor
• Technical aspects of technique
• Factor extraction
• Factor rotation
• Number of factors

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Left-right scale

• Ordinary working people do not get their fair
  share of the nations wealth
• Big business benefits owners at the expense of
  workers
• Government should redistribute income from the
  better-off to those who are less well off
• There is one law for the rich and one for the
  poor
• Management will always try to get the better of
  employees if it gets the chance

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Liberal-Authoritarian scale

• Censorship of films and magazines is necessary to
  uphold moral standards
• Schools should teach children to obey authority
• Young people today dont have enough respect for
  traditional British values
• People who break the law should be given stiffer
  sentences
• For some crimes, the death penalty is the most
  appropriate sentence
• The law should always be obeyed even if a
  particular law is wrong

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Initial Analysis

• Two factor structure confirmed
• Not sensitive to technical issues
• Extraction method
• Rotation procedure
• But what about new issues?

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New issue

• Additional item
• Refugees who are in danger because of their
  political beliefs should always be welcome in
  Britain
• How does this item relate to the other two scales?

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Additional item

• Three factor solution
• Third factor suggests liberal-authoritarian
  values may be multi-faceted
• Are left-right values also multi-faceted?

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Additional measures

• Its only right that taxes paid by the majority
  help support those in need
• If we want to live in a healthy, well-educated
  society we have to be willing to pay the taxes to
  find it.
• Its not fair that some people pay a lot of money
  in tax and hardly use the services their taxes
  pay for
• The best reason for paying taxes now is that you
  never know when you might need benefits and
  services yourself
• Its not right that people benefit from services
  they havent helped to pay for
• Inequality continues to exist because it benefits
  the rich and powerful

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EFA Summary

• Technical issues have relatively small impact
• Data issues very important for secondary analysis
• Interpretation of factors requires caution!

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Confirmatory Factor Analysis

• Posits a structure and assesses goodness of fit
  of structure to data
• Formal goodness of fit statistics allow for
  comparison between groups (years)

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Learning CFA

• Very different approach than EFA
• Despite similarities in underlying methods
• Requires specialist software
• Availability
• Training
• May be little support within institutions

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Model structure
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Model fit
0.06
0.95
RMSEA
CFI
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Modification

• Period 1986-1995 all years acceptable fit between
  model and data
• Period 1996-2005 less acceptable fit, in 1998,
  2001, 2002 and 2005 fit is not acceptable. Why?
• Modification indexes gt cross-loading between
  redistribution and liberal-authoritarian scale

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Modified model

• Acceptable fit in each year
• Measurement invariance
• Configural invariance
• Weak measurement invariance
• 1986 used as base-line
• Compared each year to 1986

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Measurement Invariance

• For each year both configural and weak
  measurement invariance models fit data
• Suggests that the structure of attitudes is not
  significantly different between 1986 and 2005
• Good news! Expect core values to be stable but
  not the whole story.

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Redistribution loading on left-right scale
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Death penalty loading on Lib-Auth scale
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Redistribution cross-loading
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Scale correlation
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Conclusions

• Undoubtedly Factor Analysis the right approach to
  the initial research questions
• EFA helped to understand the structure but very
  sensitive to the available measures
• Be wary of SPSS defaults
• CFA may be difficult to interpret model fit
  data, especially with large sample sizes and/or
  many groups for comparison.
• Can be daunting to learn, especially new software