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We discuss the problem of random measurement error in two variables when using a cross-lagged panel design. We apply the problem to the question of the causal direction between socio-economic status and subjective health, known also as health selection versus social causation. We plot the bias of the ratio between the social causation and the health selection coefficient as a function of the degree of measurement error in subjective health and socio-economic status for different scenarios which might occur in practice. Using simulated data we give an example of a Bayesian model for the treatment of measurement error that relies on external information about the degree of measurement error.
Kröger, H., Hoffmann, R., & Pakpahan, E. (2016). Consequences of measurement error for inference in cross-lagged panel design-the example of the reciprocal causal relationship between subjective health and socio-economic status. Journal of the Royal Statistical Society. Series A: Statistics in Society, 179(2), 607–628. https://doi.org/10.1111/rssa.12129