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Two-wave Two-variable Models. David A. Kenny. The Basic Design. Two variables Measured at two times Gives rise to 4 variables Say Depression and Marital Satisfaction are measured for wives with a separation of one year. We have D 1 , D 2 , S 1 , and S 2.

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the basic design
The Basic Design
  • Two variables
  • Measured at two times
  • Gives rise to 4 variables
  • Say Depression and Marital Satisfaction are measured for wives with a separation of one year.
  • We have D1, D2, S1, and S2.
standard cross lagged regression model
Standard Cross-lagged Regression Model
  • Time 1 variables cause Time 2 variables.
    • Two stabilities
      • S1  S2
      • D1  D2
    • Two cross-lagged effects
      • S1  D2
      • D1  S2
  • Time 2 disturbances correlated.
  • Inadvisable to have paths between Time 2 variables (S2  D2 or D2  S2)
causal preponderance
Causal Preponderance
  • Is S a stronger cause of D than is D of S?
  • No easy way because the units of measurement of S and D are likely very different.
  • Can standardize all the variables, but as will be seen this is more difficult when S and D are latent.
  • No measurement error in S1 and D1. (Ironically, OK if there is measurement error in S2 and D2.)
  • Nothing that causes both the time 1 variable and the time 2 variables. Such a variable is sometimes called a confounder. So if there is a gender (and gender is not controlled) difference at time 1, once we control for S1 and D1, there are no remaining gender differences at time 2 in S or D.
  • The lagged effect of variables is exactly the length of measurement.
what to do about the assumptions
What to Do about the Assumptions?
  • Measurement error in S1 and D1:
    • Latent variable analysis (discussed in a latter slide).
  • Confounders
    • Measure them.
    • Sensitivity analysis: See how the results change assuming confounders.
  • Wrong lag
    • Multi-wave study can be used to establish the optimal lag.
latent variables
Latent Variables
  • Can have as few as two indicators per latent variable.
  • Correlate errors of the same indicator measured at different times.
  • Test to see if loadings do not change over time.
causal preponderance1
Causal Preponderance
  • Note that even if the Time 1 latent variables are standardized, the Time 2 ones are not.
    • One can standardize disturbances (U and V in the figure), but cannot standardize latent endogenous variables (S2 and D2).
  • One can through a series on non-linear constraints standardized latent endogenous variables, it is very complicated.
  • However, the SEM program laavan does have an option to standardize all latent variables (
depression and marital satisfaction example
Depression and Marital Satisfaction Example
  • Gustavson, K. B. et al.  (2012). Reciprocal longitudinal associations between depressive symptoms and romantic partners' synchronized view of relationship quality. Journal of Social and Personal Relationships29, 776- 794.