Measuring Well-BeingPsychometric Perspectives

Sam Norton

sam.norton@kcl.ac.uk

18 June 2013

Overview

1 Background

2 Problems with single items and sum scores

3 Generalised latent variable modellingPositive and negative aspects of subjective well-being

4 Hierarchical modelsUsing bifactor models to parse common and specific variance

5 Conclusion

S. Norton Measuring Well-Being 18 June 2013 2 / 36

What is well-being?

I Broad constructincorporating psychological,physical, social andmaterial/economiccomponents

I Poorly defined and typicallyoperationalised in a varietyof ways

I Focus on subjective andpsychological well-being

S. Norton Measuring Well-Being 18 June 2013 3 / 36

Public policy

I GDP and life satisfaction

S. Norton Measuring Well-Being 18 June 2013 4 / 36

Subjective and psychological well-being

I Subjective well-beingI Hedonic well-being – focussed on pleasure and affectI Ed Diener – Incorporates positive and negative affect, and life

satisfactionI Psychological well-being

I Based on Aristotelian concept of eudaimonic well-being – ‘thegood life’

I Carol Ryff – self-acceptance, personal growth, purpose in life,positive relations with others, environmental mastery andautonomy

I Martin Seligman – Authentic happiness model emphasisingfinding meaning in life

I Most health research focuses on the negative end ofsubjective well-being → negative affect

S. Norton Measuring Well-Being 18 June 2013 5 / 36

Issues with measuring subjective well-being

I Not directly observableI Positive or negative emphasisI Scope → very general / very specificI State vs traitI Evaluative or affectiveI Cultural differences

S. Norton Measuring Well-Being 18 June 2013 6 / 36

Issues to focus on today

I Problems with single items and sum scoresI Generalised latent variable modellingI Hierarchical models

S. Norton Measuring Well-Being 18 June 2013 7 / 36

Latent variables

I Observed variables used tomeasure something not directlyobservable

I Recovered from the commonvariance (co-variance) betweenitems

I Ubiquitous in statistics, not justpsychometrics

S. Norton Measuring Well-Being 18 June 2013 8 / 36

Problems with single items

I Perceived issues, compared to multi-item scalesI Poor reliabilityI Less validity

I More important issuesI Problems with scaling → restricted response categories,

skewed response distributionI Can’t partition response variance into common variance,

unique variance and measurement error

I Single items fine in many circumstances where a generale.g. life satisfaction

S. Norton Measuring Well-Being 18 June 2013 9 / 36

Problems with sum scores

I Still common practice to sum (or average) responses onmulti-item scales

I Increased reliability and validity compared to single itemsI Reliability is an issue for short scales, leads to redundant or

similar items being includedI Restrictive assumptions needed to allow comparison across

samples (classical test theory)I Appropriate to sum scores of items with binary/ordinal

response formats and treat this total score as continuous?

S. Norton Measuring Well-Being 18 June 2013 10 / 36

Issues to focus on today

I Problems with single items and sum scoresI Generalised latent variable modellingI Hierarchical models

S. Norton Measuring Well-Being 18 June 2013 11 / 36

Two alternative methods

I Factor analysisI Items measured on a continuous scale (multivariate normal)I Factor loadingsI Allows for a more precise estimate of reliability than

Chronbach’s αI Item response theory

I Binary or ordinal response scaleI Item difficult and discrimination parametersI Information function provides a more sophisticated insight into

reliability than Factor analysis

I Not quite so different!

S. Norton Measuring Well-Being 18 June 2013 12 / 36

Measurement models

Confirmatory factor analysis= linear regression

F

y1

y2

y3

e1

e2

e3

λ1

λ2

λ3

Item response theory= logistic regression

F

y∗1

y∗2

y∗3

y1

y2

y3

e1

e2

e3

λ1

λ2

λ3

S. Norton Measuring Well-Being 18 June 2013 13 / 36

Generalised latent variable modelling

I Standard CFA and IRT models subsumed within a family ofgeneralised latent variable models

I Increasing number of stats packages available to fit thesekinds of models

I Mplus, GLLAMM, R, Mx, Factor . . . Stata v13

S. Norton Measuring Well-Being 18 June 2013 14 / 36

Positive and negative aspects of subjectivewell-being

I Most health research focuses on the negative end ofsubjective well-being → negative affect

I Evidence of independence of positive and negative affectI Comparison of two scales, assuming unidimensionality

I Hospital Anxiety and Depression Scale – 7-item depressionsubscale with 4-point ordinal response format

I Cardiovascular disease, N = 893I Chronbach’s α = .83

I Short Depression Happiness Questionnaire – 6-item scale with4-point ordinal response format

I General population, N = 1262I Chronbach’s α = .88

S. Norton Measuring Well-Being 18 June 2013 15 / 36

The problem with focussing on the negative

Two parameter logistic model fitted for each scale using Mplus

Item LoadingHADS2 0.760HADS4 0.795HADS6 0.625HADS8 0.414HADS10 0.576HADS12 0.722HADS14 0.418

Item LoadingSDHS1 0.855SDHS2 -0.884SDHS3 0.769SDHS4 -0.824SDHS5 -0.933SDHS6 0.805

S. Norton Measuring Well-Being 18 June 2013 16 / 36

Item characteristic curves

I Hospital Anxiety and Depression Scale - Depression subscale

S. Norton Measuring Well-Being 18 June 2013 17 / 36

Item characteristic curves

I Short Depression Happiness Questionnaire

S. Norton Measuring Well-Being 18 June 2013 18 / 36

Test information function

I Hospital Anxiety and Depression Scale - Depression subscale

S. Norton Measuring Well-Being 18 June 2013 19 / 36

Test information function

I Short Depression Happiness Questionnaire

S. Norton Measuring Well-Being 18 June 2013 20 / 36

Independent constructs

I So far have assumed positive and negative affect two ends ofa continuum

I Evidence of independence of positive and negative affectI Analysis of the SDHS reveals two factor positive–negative

structure provides ‘better fit’, however correlation betweenfactor is .86

I CFA useful for testing latent structure against theory

S. Norton Measuring Well-Being 18 June 2013 21 / 36

Issues to focus on today

I Problems with single items and sum scoresI Generalised latent variable modellingI Hierarchical models

S. Norton Measuring Well-Being 18 June 2013 22 / 36

Hierarchical models

I Most CFA studies focus on separate correlated factorsI Often theoretically salient higher-order constructs, or high

inter-factor correlations indicating factors are not entirelyindependent

I Two approaches to modelling hierarchical structureI Higher-orderI Bifactor

S. Norton Measuring Well-Being 18 June 2013 23 / 36

Higher-order vs bifactor models

F2

F1

G

F2

F1

G

S. Norton Measuring Well-Being 18 June 2013 24 / 36

HADS meta CFA

I Norton et al (2013). Journal of Psychosomatic ResearchI Hospital Anxiety & Depression Scale, 14-items split across two

subscalesI Twenty-one studies, provided data from 28 unique samples

(N = 21, 820)I Compared ‘best fit’ latent structures previously identified plus

bifactorI Re-analysis and multivariate meta-analysis

S. Norton Measuring Well-Being 18 June 2013 25 / 36

HADS Meta CFA model fit

RMSEA CFI TLI BIC1. Unidimensional 0.089 0.863 0.838 7827712. Zigmond & Snaith 0.058 0.943 0.932 7749458. Higher-order 0.053 0.953 0.943 7739639. Bifactor 0.043 0.974 0.963 771965

S. Norton Measuring Well-Being 18 June 2013 26 / 36

Implications for mood disorders

Watson, D. (2005). Journal of abnormal psychology, 114(4), 522

S. Norton Measuring Well-Being 18 June 2013 27 / 36

DSM-V Reliability

Am J Psychiatry. 2013;170(1):1-5

S. Norton Measuring Well-Being 18 June 2013 28 / 36

DSM-V Reliability

S. Norton Measuring Well-Being 18 June 2013 29 / 36

DSM-V Reliability

S. Norton Measuring Well-Being 18 June 2013 30 / 36

Well-being in general

I So far have shown bifactor model useful applied to symptomsof anxiety and depression

I Also evidence of its applicability more widely to well-beingI Chen et al (2012) evidence of a general

psychological/subjective well-being factorI 795 university studentsI Examined bifactor models for subjective well-being,

psychological well-being and a combined well-being model

S. Norton Measuring Well-Being 18 June 2013 31 / 36

Chen et al (2012) subjective well-beingRMSEA = .054 (CI: .047 to .062), SRMR = .026, CFI = .974

S. Norton Measuring Well-Being 18 June 2013 32 / 36

Chen et al (2012) psychological well-beingRMSEA = .075 (CI: .071 to .079), SRMR = .045, CFI = .908

S. Norton Measuring Well-Being 18 June 2013 33 / 36

Chen et al (2012) combined well-beingRMSEA = .061 (CI: .058 to .063), SRMR = .051, CFI = .900

S. Norton Measuring Well-Being 18 June 2013 34 / 36

Conclusions

I Well-being a broad concept incorporating psychological,physical, social and material

I Single items are fine in some circumstancesI Avoid use of sum scores where possible, instead use factor

scoresI Tests do not have to be long → Computer adaptive testingI Generalised latent variable modelling offers advantages over

over traditional CFA → best of both worldsI Think carefully about what you want to measure (and how to

measure it)!

S. Norton Measuring Well-Being 18 June 2013 35 / 36

Thank you, any questions?

S. Norton Measuring Well-Being 18 June 2013 36 / 36