Using repeated measures data to analyse reciprocal effects:

the case of Economic Perceptions and Economic Values

Patrick Sturgis, Department of Sociology, University of Surrey

Peter Smith, Ann Berrington, Yongjian Hu, Department of Social Statistics, University of

Southampton

Reciprocal Causality

Often viewed as a ‘nuisance’ to be removed (simultaneity bias).

But can be of substantive and policy interest.Achievement/self-esteem

Anti-social behaviour/depression

Problematic to estimate with observational data.

Overview

Approaches to estimating reciprocal effects.General Linear ModelInstrumental variable approachesCross-lagged panel models

Errors of MeasurementUnobserved variables and error covarianceExample: economic values and perceptionsConclusions

‘True’ Model

X Y

a

b

Standard Approach X-Sectional Data

Y X

e

Y X

e

c

(Ignore the problem)

c = f(a + b)

Instrumental Variables Approach

d1

X Y

d2

Instruments Instruments

cross-lagged panel model

cross-lagged panel model (Campbell 1960; Campbell and Kenny 1999; Finkel 1995; Marsh and Yeung 1997).

Particularly useful for examining questions of reciprocal causality.Each Y variable is regressed onto its lagged measure and the lagged measure of the other Y variable(s) of interest.Can the history of X predict Y, net of the history of Y (Granger causality)?Problematic for correlational designs (Rogossa 1995).But with SEM it is much more powerful (Marsh 1993; 1997).

Cross-lagged Panel Model

Yt1Yt0

Xt1Xt0

d11

d21

Problems with this model

2 waves = limited information about causal relationship.

Concepts are assumed to be measured with zero error.

No account taken of correlations between disturbances of endogenous variables.

Consequences of Measurement Error

All measurements of abstract concepts will contain error.

Error can be stochastic ( ) or systematic ( ) .Systematic error biases descriptive and causal

inferences.Stochastic error in dependents leaves

estimates unbiased but less efficient.Stochastic error in independents attenuates

effect sizes.Both problematic for hypothesis testing and

causal inference.

Correction for Measurement Error

Specify each concept of interest as a latent variable with multiple indicators:

Xt1

e1 e2 e3

item1t1 item2t1 item3t1

Xt2

e4 e5 e6

item1t2 item2t2 item3t2

Specify error covariance structure:

d1

Correlated Disturbances 1

The disturbance terms for the same endogenous variable over time are likely to be correlated.

Similarly, the disturbance term for the 2 endogenous variables are likely to be correlated at the same time point.

Caused by unobserved variable bias; a third variable, Z, may be causing both Y variables simultaneously.

Failing to consider these parameters can bias stability and cross-lagged estimates (Williams & Posakoff 1989; Anderson & Williams 1992).

Y11Y10

Y21Y20

Y12

Y22

d21 d22

d11 d21

Correlated Disturbances 2

Example: Economic Perceptions & Values

Left-right economic value posited as fundamental explanatory variable for political preferences & vote (Feldman 1989; Bartle 2000).

Similarly, perceptions of economic performance are seen as crucial determinants of electoral outcomes (Lewis-Beck & Stagmaier 2000).

What is the relationship between them? Different macro-economic conditions require

different approaches to economic policy.People’s left-right leanings are likely to influence

their perceptions of economic performance (Evans and Andersen 1997).

Data and Measures

Data come from the 1992-1997 British Election Panel Study.

Analytical sample = those interviews at all five waves (n=1640).

Left-right value measured by 6 item scale (Heath et al 1993).

Economic perceptions measured by 3 items tapping retrospective (past year) perceptions of:

• Level of unemployment• Rate of inflation• Standard of living

Cross-sectional Model

ECONP92 LEFRI92

e1

.38

ECONP92 LEFRI92

e1

.38

ECONP92 LEFRI92

e1e2

TORY92LAB92HHINC92

IV Model

.50

.67

.12.17

-.31

Cross-lagged Observed Score Model

ECONP94

ECONP92

LEFRI94

LEFRI92

e7e8

.04 .26.26 .68

Cross-lagged latent 2 wave

1.01

.58

.12

.53

.97

.48

-.10

.27econ92

y31

e3

y21

e2

y11

e1

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x11

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x21

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lr94

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x63

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d3

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etc.

Cross-lagged latent 5 wave

a a

b b

c c

d d

Cross-lagged latent Pooled Effect(zero disturbance covariances)

Path 92-94 94-95 95-96 97-97 Value -> Value .91* .91* .90* .86* Value -> Perceptions .33* .28* .25* .22* Perceptions -> Perceptions .59* .69* .70* .71* Perceptions -> Value .07* .09* .11* .11*

Chi Square = 2671 df=1024 p<0.001

IFI = .938; RMSEA = .031

econ92

y31

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y21

e2

y11

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lr92

x11

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x62

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econ95

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y13

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lr95

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x43

e23

x53

e24

x63

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d3

d4

Cross-lagged latent 5 wave(correlated disturbances)

Cross-lagged latent Pooled Effect(disturbance covariances estimated)

Path 92-94 94-95 95-96 97-97 Value -> Value .93* .95* .95* .93* Value -> Perceptions .21* .19* .17* .15* Perceptions -> Perceptions .65* .75* .76* .76* Perceptions -> Value .02 .02 .03 .03

Chi Square = 2537 df=1050 p<0.001

IFI = .943; RMSEA = .029

Summary of Cross Lagged Effect Estimates

Model Number Path 1 2 3 4 5 6 7 Value -> Perceptions .38 .50 .26 .53 .48 .3 .18 Perceptions -> Value .38 .67 .04 .12 n.s. .1 n.s.

Conclusions

Reciprocal relationships can be seen as either a nuisance or of substantive interest.

Either way, they are hard to model with observational data.

Repeated measures data offers significant leverage relative to x-sectional.

Problems of error variance and covariance much greater with panel data.

Need to correct for errors in the measurement of abstract concepts.

And estimate relationships between measurement errors over time.

Conclusions

Unobserved variable bias likely to manifest through covariance between residuals.

Failure to model these errors and their covariance structures can lead to seriously biased causal inference.

Naïve analyses showed strong non-recursive relationship between economic values and perceptions.

More appropriate treatment of error structures altered causal inference substantially.