Post on 18-Dec-2015
Using Exploratory and Confirmatory Factor Analysis to Understand Social Attitudes
Paula SurridgeDept. of Sociology
University of Bristolp.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 -0.046
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 0.095
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 0.106
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
Left-right
Lib-Auth
wealth e1
1
1
BigBusnN e21
redistrb e31
RichLaw e41
Indust4 e51
censor e6
1
1
Obey e71
tradvals e91
StifSent e101
DeathApp e111
Model structure
Model fit
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
1986
1987
1989
1990
1991
1993
1995
1996
1998
1999
2000
2001
2002
2003
2004
2005
RMSEA
0.06
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1986
1987
1989
1990
1991
1993
1995
1996
1998
1999
2000
2001
2002
2003
2004
2005
CFI
0.95
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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1986
1987
1989
1990
1991
1993
1995
1996
1998
1999
2000
2001
2002
2003
2004
2005
Death penalty loading on Lib-Auth scale
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1986 1987 1989 1990 1991 1993 1995 1996 1998 1999 2000 2001 2002 2003 2004 2005
Redistribution cross-loading
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
1986
1987
1989
1990
1991
1993
1995
1996
1998
1999
2000
2001
2002
2003
2004
2005
Scale correlation
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1986
1987
1989
1990
1991
1993
1995
1996
1998
1999
2000
2001
2002
2003
2004
2005
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