Table 1 The comparison of different analysis approaches
Approaches | Model | Estimand | Ability to solve unobserved time-invariant confounding |
|---|---|---|---|
Concurrent change-change analysis | \({\varDelta Y}_{1}=\widehat{\alpha }+\widehat{\beta }{\varDelta X}_{1}+\widehat{\gamma }{\varDelta Z}_{1}\) | Concurrent effect | Yes |
Change-score analysis | \({\varDelta Y}_{1}={\widehat{\alpha }}^{*}+{\widehat{\beta }}^{*}{X}_{0}+{\widehat{\gamma }}^{*}{Z}_{0}\) | One-period lagged effect | No |
Lagged change-change analysis | \({\varDelta Y}_{2}={\widehat{\alpha }}^{**}+{\widehat{\beta }}^{**}{\varDelta X}_{1}+{\widehat{\gamma }}^{**}{\varDelta Z}_{1}\) | One-period lagged effect | Yes |