Measurement models Subjective Well-being in Later Life

Dr. Bram Vanhoutte

CCSR, University of Manchester

5 Dec 2013 - methods@manchester

Latent variables in health inequalities research

Overview

• Intro – Why do we need measurement models?

• Theory – How do measurement models work?

• Practice – Which programs?

• Example – Subjective wellbeing in later life

• Some conclusions

A. Intro Why do we need measurement models?

A) Because (social) scientists often work with ‘invisible’, (unobservable, latent) concepts, measured through multiple observed indicators

– Example Depression

• Straightforward question might not “work”

• Refer to symptoms such lack of sleep, feeling down, low energy, feeeling as if everything is an effort, feeling sad…

A. Intro Why do we need measurement models?

B) Because the way we measure a concept matters, introduces “error” (which can be modelled!)

– Example:

• Acquiescence: tendency to say yes

• Counter with negatively worded items…

• But then meaning of item changes!

A. Intro Why do we need measurement models?

C) Sets the stage for more advanced questions:

– What’s the structure of the latent concept

• Number of dimensions, hierarchical structure?

– Do different groups answer in the same way

• Equivalence of measures across gender, agegroups, countries

B. Theory Notation

Latent variables, factors, constructs

Observed variables, measures, indicators, manifest variables

Direction of influence, relationship from one variable to another

Association not explained within the model

η & ξ

x & y

λ & β

ζ Unexplained Error in Model

δ & ε Measurement Errors

• Two forms of factor analysis, both aimed at reducing (observed) data (into latent constructs)

• EFA is seen as data driven, and CFA as theory driven (BUT)

• EFA useful to determine number of factors and explore which item belongs where.

• This presentation focuses on CFA

B. Theory Exploratory VS Confirmatory?

A Confirmatory Factor Model

An Exploratory Factor Model

1. Define a model

• Map items onto latent concept

• Model error?

2. Test how good a model fits the data

3. Evaluate model

• Substantively

• Statistically

4. Adapt?

B. Theory CFA / Measurement analysis:

Simple Example: Trust in Individuals

δξΛx x

Trust in Individuals

people aren’t

helpful

(x1)

people can

not be trusted

(x2)

people are

Fair

(x3)

1

ξ1

δ1 δ2 δ3

21212 x

313 x

)( 111 VAR

)(00

)(0

)(

3

2

1

VAR

VAR

VAR

λ11 λ21

11111 x

B. Theory Simple CFA

• Latent concept(s) and observed measures mapped beforehand

• Usually indicators only load on 1 latent construct (no crossloadings)

• 1 parameter already defined (“fixed”) • Indicator is “caused” by latent concept and

error • Error terms uncorrelated

• Model based on variance covariance matrix

B. Theory Model Identification

• To estimate the parameters of a model, it needs to be at least just identified.

• This means there are as least as much unknowns (parameters to be estimated) as there are knowns (var and covar)

• Knowns = p(p+1)/2 , where p = number of observed vars

• To estimate model fit, we need over-identification, for ex. 3 indictors for one latent factor

1. Define a model

• Map items onto latent concept

• Model error?

2. Test how good a model fits the data

3. Evaluate model

• Substantively

• Statistically

4. Adapt?

B. Theory CFA / Measurement analysis:

• Originally: chi square test + degrees of freedom – With large samples trivial differences become significant

• Absolute measures of fit – How good does model reproduce the data?

– Root Means Square Error of Approximation (RMSEA)

• Good fit =<.08 , Excellent fit =<.06

• Incremental fit indexes – Where is model situated between best model and baseline

model

– Comparative Fit Index (CFI) , good fit >.90 , Excellent >.95

B. Theory Model fit indexes

1. Define a model

• Map items onto latent concept

• Model error?

2. Test how good a model fits the data

3. Evaluate model

• Substantively

• Statistically

4. Adapt?

B. Theory CFA / Measurement analysis:

• Model doesn’t seem to fit !

– Double check everything (sample used for estimation/model specified/item coding/…)

– What does theory say?

• Other models?

• Possible measurement effects ?

– What do the stats say?

• Do parameters make sense?

• Is your fit way off, or near the boundaries of acceptability

• Modification indexes flag parameters “under pressure”

– Adapt model ?

B. Theory Model evaluation

1. Define a model

• Map items onto latent concept

• Model error?

2. Test how good a model fits the data

3. Evaluate model

• Substantively

• Statistically

4. Adapt?

B. Theory CFA / Measurement analysis:

Simple Example: Trust in Individuals

δξΛx x

Trust in Individuals

people aren’t

helpful

(x1)

people can

not be trusted

(x2)

people are

Fair

(x3)

1

ξ1

δ1 δ2 δ3

21212 x

313 x

)( 111 VAR

)(00

)(0

)(

3

2

1

VAR

VAR

VAR

λ11 λ21

11111 x

C. Practice

• Different programs can be used for CFA

– Mplus, AMOS, Stata (a bit), LISREL, EQS, R

-->Structural equation modeling software

– Mplus most advanced and many possibilities, but requires some learning and gives extensive output.

– Stata add-on “runmplus”

– Possible to do path analysis, growth curve analysis, multilevel analysis as well

•

D. Example

• Measuring subjective wellbeing in later life

– Investigate concept of later life wellbeing

– using common measures of well-being

– in a second order factor analysis

Epicurus/Aristippus Aristotle

Hedonic well-being

• Philosophical roots in Aristippus of Cyrene, Epicurus, Bentham, Mill

– Well-being is maximalisation of pleasure, minimalisation of suffering

• Affective and cognitive aspect (Diener 1984)

– Both + and – affect, based on moods and emotions

– Individual assessment of quality of life, based on internal criteria (Life satisfaction)

Hedonic

Well-being

Positive

Affect

Affective Cognitive

+ -

Negative

Affect

CES-D SWLS

Domain

specific Holistic

Hedonic Well-being

Eudemonic well-being

• Different operationalisations, with similar subdimensions: – Psychological Well-being (Ryff & Singer, 1998) – Self-determination Theory (Ryan & Deci, 2000) – In later life: CASP (Hyde, Wiggins, Higgs & Blane, 2003)

• Philosophical roots in Aristotle: • Well-being is about developing one-self and realising one’s potential (Maslow 1968; Erikson 1959)

Eudemonic Well-being

Eudemonic

Well-being

Autonomy & Self-

realisation Control Pleasure

CASP CASP15

Data + methods

• Data:

– English Longitudinal Study of Ageing, age 50+

– Wave 3 Self-completion questionnaire (n=8244)

• Second order cfa

– First establish first order constructs

– Then investigate second order constructs (=factors that determine first order factors)

Examine first order factors: CES-D • CES-D :

– Theory : Depression in later life is commonly more somatic and less severe, symptoms might also be due to stresses of later life rather than depression

• =>1 or 2 dimensions?

• =>Measurement effects negative items?

CES-D

x1 x2 x6

δ1 δ2 δ6

x7

δ7

… x1 x2 x3

δ1 δ2 δ3

Mood

x4 x5 x6

δ4 δ5 δ6

x7

δ7

OR Somatic

Outcome CES-D first order analysis

RMSEA CFI

1 factor (Depressive Symptoms) .077 .971

With error correlations .065 .981

2 factors (Somatic / Mood Symptoms) .053 .987

With error correlations .035 .995

•Test different models in a CFA framework •Examine outcomes and fit statistics

Possible Second order Models

Model 1 Model 2 Model 3 Model 4

GHQ Anxiety

Subjective Well-

being

Hedonic Well-

being

Affective Well-

being

Hedonic Affective

Well-being

GHQ Social

dysfunction

GHQ Loss of

confidence

CES-D Somatic

CES-D Mood

SWLS Present

Cognitive Well-

being

Hedonic Cognitive

Well-being SWLS Past

CASP Control

&Autonomy

Eudemonic Well-

being

Eudemonic Well-

being CASP Self-

Realisation

CASP Pleasure

Second order Results

RMSEA CFI

Model 1 – 1 dimension of SWB 0.080 0.902

Model 2 – 2 dimensions: hedonic/eudemonic 0.075 0.913

Model 3 – 2 dimensions: affective/cognitive 0.062 0.940

Model 4 – 3 dimensions:

affective/cognitive/eudemonic 0.057 0.951

Although all models show acceptable fit, best fit is three dimensional model

3 Dimensional Second Order Model

Conclusions example

• 3 dimensional model of wellbeing in later life, distinguishing emotional, cognitive and eudemonic aspects of wellbeing

• Strong relation between cognitive and eudemonic measures, slightly weaker relationship of both concepts with affective wellbeing

– > satisfaction and autonomy do not necessarily mean the same thing as good mental health

Conclusions in general Measurement models

• Transforms multiple categorical indicators in

an (interval) latent variable

• Inform us about the structure of the concepts we use and test substantial theory

• Make it possible to model measurement effects and reduce measurement error

• Starting point more than endpoint ?

Want to learn more ?

• Mplus online tutorials are quite good to learn the ropes

– More info on statmodel.com

• There is a one day short course on latent factor analyses I will be giving on februar 7th

– More info on ccsr.ac.uk/courses