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Covariate adjustment can cost precision under unequal allocation

Source: R/ledger_scan2.R
morie_adjustment_variances.Rd

Superpopulation asymptotic variances (times \(n\)) with arm slopes b1, b0, noise variances v1, v0 and treated share p: unadjusted, pooled-slope ANCOVA and Lin's interaction estimator (Research.P3.Adjustment.adjusted_minus_unadjusted, lin_le_unadjusted, lin_le_adjusted); with b0 = 0 the pooled adjustment is worse than none iff \(p > 2/3\) (adjusted_worse), never at \(p = 1/2\) (adjusted_le_unadjusted_balanced).

Usage

morie_adjustment_variances(b1, b0, v1, v0, p)

Arguments

b1, b0

Slopes of the potential outcomes on the centred unit-variance covariate.

v1, v0

Noise variances.

p

Treated share in (0, 1).

Value

A list: unadjusted, adjusted, lin, adjusted_minus_unadjusted and adjustment_hurts.

References

Freedman DA (2008). On regression adjustments to experimental data. Advances in Applied Mathematics 40(2). Lin W (2013). Agnostic notes on regression adjustments to experimental data. Annals of Applied Statistics 7(1).

Examples

morie_adjustment_variances(b1 = 1, b0 = 0, v1 = 1, v0 = 1, p = 0.8)
#> $unadjusted
#> [1] 7.5
#> 
#> $adjusted
#> [1] 9.5
#> 
#> $lin
#> [1] 6.25
#> 
#> $adjusted_minus_unadjusted
#> [1] 2
#> 
#> $adjustment_hurts
#> [1] TRUE
#> 
#> attr(,"theorem")
#> [1] "Research.P3.Adjustment.adjusted_minus_unadjusted"