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Cross-lagged Panel Models

Cross-lagged Panel Models. Patrick Sturgis, Department of Sociology, University of Surrey. Overview. Autoregressive model Cross-lagged panel model Multiple indicator model Correlated disturbances Example: membership and social trust Limitations Summary. Autoregressive (Simplex) Model.

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Cross-lagged Panel Models

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  1. Cross-lagged Panel Models Patrick Sturgis, Department of Sociology, University of Surrey

  2. Overview • Autoregressive model • Cross-lagged panel model • Multiple indicator model • Correlated disturbances • Example: membership and social trust • Limitations • Summary

  3. Autoregressive (Simplex) Model • Repeated measures of a variable expressed as function of preceding value plus random disturbance: • Where the represents the overtime stability of • This is a univariate autoregressive model

  4. Autoregressive (Simplex) Model • Can be represented as a path diagram: • y1 is treated as predetermined

  5. Cross-lagged panel model • Univariate simplex model can be extended to the bivariate case • Cross-lagged panel model (Campbell 1960; Campbell and Kenny 1999; Finkel 1995; Marsh and Yeung 1997) • Also called residualised regression, endogenous regressor models, transition models • Often used for examining questions of reciprocal causality

  6. Cross-lagged panel model • Each variable in the system is regressed onto its lagged measure and the lagged measure of the other variable(s) of interest. • Can the history of X predict Y, net of the history of Y (Granger causality)? • Generally estimated via ML, though estimators for non-MVN available • SEM framework enables some powerful extensions to the basic model

  7. Cross-lagged panel model

  8. Cross-lagged Panel Model = = Structural parameters may be constrained to equality over time

  9. Dealing with 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. • SEM framework allows for error correction models via multiple indicators

  10. e1 e4 e2 e5 e3 e6 x12 x11 x22 x21 x31 x32 y1 y2 Correction for Measurement Error Specify each concept of interest as a latent variable with multiple indicators: Specify error covariance structure: d1

  11. Factorial Invariance = = Constrain same loading to be equal over time

  12. 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 may 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).

  13. d11 d12 Y1 Y2 Y0 w1 w2 w0 d21 d22 Correlated Disturbances 2

  14. Example: Membership and Trust • Civic participation breeds interpersonal trust (Toqueville 1840, Putnam 2000) • Much x-sectional evidence supports this idea • Membership of civic associations highly correlated with trust • But what if ‘trusters’ are more likely to become members? • A virtuous circle of increasing social capital?

  15. Data and Measures • Data come from the British Household Panel Study, waves 1997-2003 • Analytical sample = those interviews at all waves from 1991-2003 (n=4650). • Membership measured as latent variable from 10 membership indicators using 2 parameter IRT models (Li, Savage and Pickles 2004). • Social trust measured using standard single indicator: • “Generally speaking, would you say that most people can be trusted, or that you can’t be too careful in dealing with people?”

  16. Results

  17. Limitations • The lagged endogenous variable provides some protection against unit heterogeneity • Fixed characteristics of individuals, some of which may be unobserved… • …and correlated with change on Y and W • Thus, the cross-lagged associations could be spurious, caused by unobserved Z • Can add Time Varying and Time Invariant covariates • But this makes model very complex and does not eradicate unit heterogeneity problem • This pm we look at more effective solution.

  18. Summary • Cross-lagged model is useful way of addressing issues of reciprocal causality with panel data • SEM framework allows error correction, factorial invariance, correlated disturbances, overall model fit assessment, categorical endogenous variables, missing data, sample weights and complex sample designs, nested model testing • Provides some protection against unit heterogeneity • But still open to possibility that cross-lagged effects are spurious

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