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