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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

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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.

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Overview Approaches to estimating reciprocal effects. General Linear Model Instrumental variable approaches Cross-lagged panel models Errors of Measurement Unobserved variables and error covariance Example: economic values and perceptions Conclusions

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True Model XY a b

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Standard Approach X-Sectional Data YX e YX e c (Ignore the problem) c = f(a + b)

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Instrumental Variables Approach d1d1 XY d2d2 Instruments

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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).

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Cross-lagged Panel Model Y t1 Y t0 X t1 X t0 d 11 d 21

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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.

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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.

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Correction for Measurement Error Specify each concept of interest as a latent variable with multiple indicators: Xt1 e1e2e3 item1t1item2t1item3t1 Xt2 e4e5e6 item1t2item2t2item3t2 Specify error covariance structure: d1

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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).

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Y 11 Y 10 Y 21 Y 20 Y 12 Y 22 d 21 d 22 d 11 d 21 Correlated Disturbances 2

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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. Peoples left-right leanings are likely to influence their perceptions of economic performance (Evans and Andersen 1997).

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Data and Measures Data come from the 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

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Cross-sectional Model

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IV Model

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Cross-lagged Observed Score Model

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Cross-lagged latent 2 wave econ92 y31 e3 y21 e2 y11 e1 lr92 x11 e4 x21 e5 x31 e6 x41 e7 x51 e8 x61 e9 econ94 y32 e18 y22 e17 y12 e16 lr94 x12 e10 x22 e11 x32 e12 x42 e13 x52 e14 x62 e15 d1 d2

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econ95 y33 e28 y23 e27 y13 e26 lr95 x13 e20 x23 e21 x33 e22 x43 e23 x53 e24 x63 e25 d3 d4 etc. Cross-lagged latent 5 wave a a bb cc d d

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Cross-lagged latent Pooled Effect (zero disturbance covariances) Chi Square = 2671 df=1024 p<0.001 IFI =.938; RMSEA =.031

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econ95 y33 e28 y23 e27 y13 e26 lr95 x13 e20 x23 e21 x33 e22 x43 e23 x53 e24 x63 e25 d3 d4 Cross-lagged latent 5 wave (correlated disturbances)

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Cross-lagged latent Pooled Effect (disturbance covariances estimated) Chi Square = 2537 df=1050 p<0.001 IFI =.943; RMSEA =.029

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Summary of Cross Lagged Effect Estimates

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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.

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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.

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