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Cross-lagged Panel Correlation (CLPC)

David A. Kenny

Example

- Depression and Marital Satisfaction measured at two points in time.
- Four measured variables S1, S2, D1, and D2.

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.

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 Z1 and Z2 is identified as rD1S2rD2S1 /(rD1S1rD2S2).

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.

Stationarity

- Define how much variance for a given a given variable, say XA, is available to correlate.
- Define the ratio of variance, time 2 divided by time 1 for XA, to be denoted as kA2.
- Given stationarity, the covariance between XA and XB at time 2 equals the time 1 covariance times kAkB.
- Also C(XA1,XB2)kB = C(XA2,XB1)kA where C is a covariance.

Basic Strategy

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

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

Example

- Test for stationarity of cross-sectional relationships:
- c2(2) = 5.186, p = .075
- Because stationarity is met, test for spuriousness:
- c2(6) = 2.534, p = .865
- Evidence consistent with spuriousness.
- Mplus syntax can be downloaded at
- www.handbookofsem.com/files/ch09/index.html

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.

In principle…

- Researchers should show that spuriousness can plausibly explain the covariation in their data.
- CLPC has a use.

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