Presentation on theme: "Cross-lagged Panel Models"— Presentation transcript:
1Cross-lagged Panel Models Patrick Sturgis,Department of Sociology, University of Surrey
2Overview Autoregressive model Cross-lagged panel model Multiple indicator modelCorrelated disturbancesExample: membership and social trustLimitationsSummary
3Autoregressive (Simplex) Model Repeated measures of a variable expressed as function of preceding value plus random disturbance:Where the represents the overtime stability ofThis is a univariate autoregressive model
4Autoregressive (Simplex) Model Can be represented as a path diagram:y1 is treated as predetermined
5Cross-lagged panel model Univariate simplex model can be extended to the bivariate caseCross-lagged panel model (Campbell 1960; Campbell and Kenny 1999; Finkel 1995; Marsh and Yeung 1997)Also called residualised regression, endogenous regressor models, transition modelsOften used for examining questions of reciprocal causality
6Cross-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 availableSEM framework enables some powerful extensions to the basic model
8Cross-lagged Panel Model ==Structural parameters may be constrained to equality over time
9Dealing 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
10Correction for Measurement Error Specify each concept of interest as a latent variable with multiple indicators:Specify error covariance structure:e1e2e3x11x21x31y2e4e5e6x12x22x32y1d1
11Factorial Invariance==Constrain same loading to be equal over time
12Correlated Disturbances 1 The disturbance terms for the same endogenous variable over time are likely to be correlatedSimilarly, 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).
14Example: Membership and Trust Civic participation breeds interpersonal trust (Toqueville 1840, Putnam 2000)Much x-sectional evidence supports this ideaMembership of civic associations highly correlated with trustBut what if ‘trusters’ are more likely to become members?A virtuous circle of increasing social capital?
15Data and MeasuresData come from the British Household Panel Study, wavesAnalytical sample = those interviews at all waves from (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?”
17LimitationsThe lagged endogenous variable provides some protection against unit heterogeneityFixed characteristics of individuals, some of which may be unobserved……and correlated with change on Y and WThus, the cross-lagged associations could be spurious, caused by unobserved ZCan add Time Varying and Time Invariant covariatesBut this makes model very complex and does not eradicate unit heterogeneity problemThis pm we look at more effective solution.
18SummaryCross-lagged model is useful way of addressing issues of reciprocal causality with panel dataSEM 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 testingProvides some protection against unit heterogeneityBut still open to possibility that cross-lagged effects are spurious