Cross lagged panel design is a type of structural equation model where information is collected at two or more points in time. It’s used primarily to assess causal relationships (which may potentially be bi-directional) in a non-experimental setting, i.e., where variables are not manipulated but simply recorded.

You would choose a cross lagged panel design when you are interested how the variables interact with each other over time. For example, you might be interested in understanding if there is a directional causation between a nation’s import levels and that nation’s poverty. Do higher levels of poverty equate to lower imports? Does lower poverty levels lead to higher imports? Or is there a bi-directionality to import levels and poverty?

Cross lagged panel design was first used in economics and then sociology, and has now spread to psychology and education as well as to behavioral science.

## The Basis of Cross Lagged Panel Design

Cross lagged panel design involves looking at two variables, X and Y, at two different times—call them 1 and 2. You’re trying to find what effect each variable has on each other at particular points in time. To do this, you combine your variables to get four new variables, or data points;

- X
_{1}, - X
_{2}, - Y
_{1}, - Y
_{2}.

These four variables might be connected by six different correlations:

- Two
*auto correlations*, - Correlation between two instances of the same variable, r
_{X1X2}and r_{Y1Y2}; - Two synchronous correlation (r
_{X1Y1}r_{X2Y2}).

In addition, there are also two *cross-lagged correlations* which we can designate r_{X1Y2}, r_{X2,Y1}. The diagram below shows the four data points and the correlations.

## Interpreting Cross Lagged Panel Design

Cross lagged panel design analysis suggests that:

- If r
_{X1Y2}is ‘substantially different’ from zero, we can conclude that X causes Y. - If r
_{X2Y1}is substantially different from zero, we can conclude that Y causes X. - If both are significantly different from zero, we conclude that X causes Y and Y causes X,
- If both are equal we conclude that they do not cause each other but are both affected by a third variable.

If we know that X and Y are correlated but our data doesn’t show any conclusive correlation between them (neither r_{X1Y2} or r_{X2Y1} are substantially different than zero) it may be that our time lag was too short (or too long) to allow causal influences to work, and we need to redesign our experiment.

## References

- Anderson & Kida. The Cross-Lagged Research Approach: Description and Illustration. Journal of Accounting Research. Vol. 20, No. 2, Part I (Autumn, 1982), pp. 403-414. Retrieved from http://www.jstor.org/stable/2490748 on May 12, 2018
- Laursen, B. et al. (2012). Handbook of Developmental Research Methods. Guilford Press.
- Tyagi & Singh. The Application of Cross-Lagged Panel Analysis In Educational Research. Facta Universitatis. Series: Philosophy, Sociology, Psychology and History. Vol 13, No 2, 2014, pp 39-51. Retrieved from http://casopisi.junis.ni.ac.rs/index.php/FUPhilSocPsyHist/article/view/151/330 on May 12, 2018.

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