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Two-wave Two-variable Models

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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Two-wave Two-variable Models

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  1. Two-wave Two-variable Models David A. Kenny

  2. 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.

  3. 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)

  4. 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.

  5. Assumptions • 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.

  6. 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.

  7. 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.

  8. 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 (std.lv=TRUE).

  9. 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.

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