Using Exploratory and Confirmatory Factor Analysis to Understand Social Attitudes

1. Using Exploratory and Confirmatory Factor Analysis to Understand Social Attitudes Paula Surridge Dept. of Sociology University of Bristol p.surridge@bris.ac.uk

2. 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

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

4. 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

5. 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?

6. 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

7. 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

8. The data • British social attitudes survey, 2004 & 2005 • Sample size ~2500 • Analysis conducted for 2004, 2005 used for validation

9. 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

10. Left-right scale • Ordinary working people do not get their fair share of the nation’s 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

11. Liberal-Authoritarian scale • Censorship of films and magazines is necessary to uphold moral standards • Schools should teach children to obey authority • Young people today don’t 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

12. Initial Analysis • Two factor structure confirmed • Not sensitive to technical issues • Extraction method • Rotation procedure • But what about ‘new’ issues?

13. ‘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?

15. Additional item • Three factor solution • Third factor suggests ‘liberal-authoritarian’ values may be multi-faceted • Are ‘left-right’ values also multi-faceted?

16. Additional measures • It’s 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. • It’s 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 • It’s not right that people benefit from services they haven’t helped to pay for • Inequality continues to exist because it benefits the rich and powerful

19. EFA: Summary • Technical issues have relatively small impact • Data issues very important for secondary analysis • Interpretation of factors requires caution!

20. 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)

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

22. Model structure

23. Model fit 0.06 0.95 RMSEA CFI

24. 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 => cross-loading between redistribution and liberal-authoritarian scale

25. Modified model • Acceptable fit in each year • Measurement invariance • ‘Configural invariance’ • ‘Weak measurement invariance’ • 1986 used as base-line • Compared each year to 1986

26. 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.

27. Redistribution loading on left-right scale

28. Death penalty loading on Lib-Auth scale

29. Redistribution cross-loading

30. Scale correlation

31. 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