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

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

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

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

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?

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

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

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

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

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

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

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

‘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?

Redistribution 0.498 -0.048 0.284 Big business 0.793 0.056 0.158 Wealth 0.817 0.017 0.008 One law for rich 0.745 -0.033 -0.163 Management 0.694 0.012 -0.189 Trad values 0.105 0.536 -0.100 Stiffer sentences 0.054 0.634 -0.202 Death Penalty 0.084 0.278 -0.492 Schools teach obey 0.005 0.611 -0.051 Law always obeyed -0.090 0.428 0.047 Censorship 0.019 0.470 0.067 Refugees 0.024 -0.011 0.593

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

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

Redistribution 0.479 -0.196 0.255 Big business 0.783 -0.044 0.101 Wealth 0.824 -0.016 -0.046 One law for rich 0.749 0.031 -0.088 Management 0.697 0.095 -0.166 Trad values 0.094 0.549 -0.073 Stiffer sentences 0.036 0.687 Death Penalty 0.103 0.532 -0.208 Schools teach obey -0.027 0.669 0.116 Law always obeyed -0.117 0.388 0.040 Censorship -0.022 0.460

Political Refugees -0.032 -0.311 0.395 Support needy 0.007 -0.025 0.647 Pay taxes for society -0.028 0.001 0.573 Pay and not use -0.036 0.274 -0.354 Never know 0.126 0.187 0.362 Benefit and not pay 0.106 0.479 -0.301 Inequality 0.603 -0.019

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

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)

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

Model structure

Model fit 0.06 0.95 RMSEA CFI

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

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

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.

Redistribution loading on left-right scale

Death penalty loading on Lib-Auth scale

Redistribution cross-loading

Scale correlation

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