Cross-lagged Panel Correlation (CLPC)

David A. Kenny

December 25, 2013

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Example• Depression and Marital

Satisfaction measured at two points in time.

• Four measured variables S1, S2, D1, and D2.

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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.

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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).

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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.

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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 kA

2.

• 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.

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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

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Example DataDumenci, 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  

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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

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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.

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In principle…• Researchers should show that spuriousness

can plausibly explain the covariation in their data.

• CLPC has a use.