Table 2.
Model Specifications
| Specification | Treatment Model | Subsample Selection Model | Outcome Model |
|---|---|---|---|
| Correct specification | A ∼ W2 | Δsub ∼ W1 + W2 | Y ∼ A + W2 + AW1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Moderately misspecified treatment | A ∼ W2mod | Δsub ∼ W1 + W2 | Y ∼ A + W2 + AW1 |
| W2mod = Sum(Z2:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Majorly misspecified treatment | A ∼ W1 | Δsub ∼ W1 + W2 | Y ∼ A + W2 + AW1 |
| W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Moderately misspecified outcome | A ∼ W2 | Δsub ∼ W1 + W2 | Y ∼ A + W2mod + AW1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2mod = Sum(Z2:Z16) | ||
| Majorly misspecified outcomea | A ∼ W2 | Δsub ∼ W1 + W2 | Y ∼ A + AW1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | |||
| Majorly misspecified outcomea | A ∼ W2 | Δsub ∼ W1 + W2 | Y ∼ A + W2 + W1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Moderately misspecified selection | A ∼ W2 | Δsub ∼ W1mod + W2 | Y ∼ A + W2 + AW1 |
| W2 = Sum(Z1:Z16) | W1mod = Sum(Z2:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Majorly misspecified selection | A ∼ W2 | Δsub ∼ W1 | Y ∼ A + W2 + AW1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | |||
| Misspecified treatment and selection | A ∼ W1 | Δsub ∼ W1 | Y ∼ A + W2 + AW1 |
| W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | |||
| Misspecified treatment and outcome | A ∼ W1 | Δsub ∼ W1 + W2 | Y ∼ A + W2 + W1 |
| W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | W2 = Sum(Z1:Z16) | ||
| Misspecified selection and outcome | A ∼ W2 | Δsub ∼ W1 | Y ∼ A + W2 + W1 |
| W2 = Sum(Z1:Z16) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) | |||
| Misspecified treatment, selection, and outcome | A ∼ W1 | Δsub ∼ W1 | Y ∼ A + W2 + W1 |
| W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | W1 = Sum(Z1:Z6) | |
| W2 = Sum(Z1:Z16) |
Abbreviations: A, treatment variable; Δsub, selection into the subsample variable; W1, summary baseline covariate; W2, summary baseline covariate; W1mod, misspecified summary baseline covariate; W2mod, misspecified summary baseline covariate; Y, outcome variable; Z, individual baseline covariate that contributes to summary baseline covariate.
a There were 2 versions of the majorly misspecified outcome model.