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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 S 1 , S 2 , D 1 , and D 2. Causal Assumptions.

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Example
Example

  • Depression and Marital Satisfaction measured at two points in time.

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


Causal assumptions
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
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
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
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
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
    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  


    Example1
    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
    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
    In principle…

    • Researchers should show that spuriousness can plausibly explain the covariation in their data.

    • CLPC has a use.


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