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Cross-Lagged Panel Correlation
Cross-lagged panels are sometimes referred to as a quasi-experimental method (non-randomized) used for longitudinal data. Correlational data measures the association, or co-variation of two or more dependent variables (see Correlational data). Cross-lagged panel correlations are used as a means to unravel the directionality in correlational research using two sets of correlations separated by a time interval. The most common approach to cross-lagged panel correlation techniques is a two-wave (T1 and T2), two-variable (X and Y) panel (2w2v) resulting in six correlations (see figure 1). The six correlations consist of two auto-correlations also referred to as the “stability” variables (rx1x2 and ry1y2), and two synchronous correlations (rx1y1 and ry2x2) and two cross-lagged correlations (rx1y2 and ry1x2). The cross-lagged correlations (rx1y2 and ry1x2) are the correlations across time and variables. When |rx1y2| > |ry1x2| the variable X is considered to be causal dominant over variable y, and when |ry1x2| > |rx1y2|  the variable Y is considered to be causal dominant over variable x (see Kenny or Locascio)

Figure 1. Cross-lagged Panel Correlation, two-wave, two variable panel.

Criticisms of Cross-Lagged Panel Correlation

The direction of causal effects is still unclear even if a difference between the cross-lagged correlations is revealed and the difference is attributed to differential causal influences between variables. In order for a cross-lagged difference to make an authoritative statement about causal direction, the effects of X on Y or vice versa would need a no-cause baseline established, however no such baseline exists. Others have suggested that the cross-lagged correlations have a masking effect of heterogeneous stabilities and as a result suggest the method should be avoided (see Rogosa). Another concern for cross-lagged panel correlations is the role of mediating variables creating spurious differences. Overall this is a good tool for ruling out third variable explanations.

Reference:

Kenny, D. A. (1975). Cross-lagged Panel Correlation: A Test for Spruousness. Psychological Bulletin. 82:6, 887-903.

Locascio, J.J. (1982). The Cross-Lagged Correlation Technique: Reconsideration in Terms of Exploratory Utility, Assumption Specification and Robustness. Educational and Psychological Measurement. 42, 1023-1036

Rogosa, D (1980). A critique of cross-lagged correlation. Psychological Bulletin. 88, 245-258.

Links:

http://frank.mtsu.edu/~sschmidt/methods/CorrelationalResearch.pdf

http://core.ecu.edu/psyc/wuenschk/SAS/ZPF.sas