1. Cross-lagged Panel Correlation (CLPC) David A. Kenny December 25, 2013

2. 2 Example Depression and Marital Satisfaction measured at two points in time. Four measured variables S 1, S 2, D 1, and D 2.

3. 3 Causal Assumptions Most analyses of longitudinal variables explain the correlation between two variables as being due to the variables causing each other: S  D and D  S. CLPC starts by assuming that the correlation between variables is not due to the two variables causing one another. Rather it is assumed that some unknown third variable, e.g., social desirability, brings out about the relationship.

4. 4 Model of Spuriousness Assume that a variable Z explains the correlation between variables at each time. The variable Z is changing over-time. The model is under-identified as a whole, but the squared correlation between Z 1 and Z 2 is identified as r D1S2 r D2S1 /(r D1S1 r D2S2 ).

5. 5

6. 6 Ruling out Spuriousness The strategy developed by Kenny in the 1970s in a series of paper is to assume stationarity. Requires at least three variables measured at each time. Stationarity –Define how much variance for a given a given variable, say D, is available to correlate. –Define the ratio of variance, time 2 divided by time 1.

7. 7 Stationarity Define how much variance for a given a given variable, say X A, is available to correlate. Define the ratio of variance, time 2 divided by time 1 for X A, to be denoted as k A 2. Given stationarity, the covariance between X A and X B at time 2 equals the time 1 covariance times k A k B. Also C(X A1,X B2 )k B = C(X A2,X B1 )k A where C is a covariance.

8. 8 Basic Strategy Test for stationarity of cross-sectional relationships. o df = n(n – 3)/2 If met, test for spuriousness. o df = n(n – 1)/2 Mplus syntax can be downloaded at www.handbookofsem.com/files/ch09/index.html

9. 9 Example Data Dumenci, L., & Windle, M. (1996). Multivariate Behavioral Research, 31, 313-330. Depression with four indicators (CESD) PA: Positive Affect (lack thereof) DA: Depressive Affect SO: Somatic Symptoms IN: Interpersonal Issues Four times separated by 6 months Use waves 1 and 2 for the example 433 adolescent females Age 16.2 at wave 1

10. 10 Example Test for stationarity of cross-sectional relationships: o  2 (2) = 5.186, p =.075 Because stationarity is met, test for spuriousness: o  2 (6) = 2.534, p =.865 Evidence consistent with spuriousness. Mplus syntax can be downloaded at www.handbookofsem.com/files/ch09/index.html

11. 11 Why is this strategy not adopted? Most researchers are interested in estimating a causal effect, not in showing you do not need to estimate any causal effects. Also, CLPC was initially proposed as way of determining causal effects, not as a way of testing of spuriousness.

12. 12 In principle… Researchers should show that spuriousness can plausibly explain the covariation in their data. CLPC has a use.