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# Cross-lagged Panel Correlation (CLPC) PowerPoint PPT Presentation

Cross-lagged Panel Correlation (CLPC). David A. Kenny. Example. Depression and Marital Satisfaction measured at two points in time. Four measured variables S 1 , S 2 , D 1 , and D 2. Causal Assumptions.

Cross-lagged Panel Correlation (CLPC)

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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

• ### 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.

• 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.