Skip to main content
. 2016 Dec 8;103(4):829–842. doi: 10.1093/biomet/asw047

Table 1.

Empirical bias Inline graphic, empirical standard error, and average estimated standard error of the estimators of Inline graphic with a continuous outcome

  Inline graphic   Inline graphic   Inline graphic
Known Inline graphic Bias ESE ASE   Bias ESE ASE   Bias ESE ASE
Inline graphic 0Inline graphic4 1Inline graphic4 1Inline graphic4   0Inline graphic1 0Inline graphic7 0Inline graphic7   0Inline graphic2 1Inline graphic7 1Inline graphic7
Inline graphic 0Inline graphic6 1Inline graphic5 1Inline graphic5   0Inline graphic1 0Inline graphic6 0Inline graphic6   0Inline graphic5 1Inline graphic6 1Inline graphic6
Inline graphic 0Inline graphic1 0Inline graphic3 0Inline graphic3   0Inline graphic0 0Inline graphic2 0Inline graphic2   0Inline graphic0 0Inline graphic3 0Inline graphic3
Correct Inline graphic Bias ESE ASE   Bias ESE ASE   Bias ESE ASE
Inline graphic 4Inline graphic1 1Inline graphic5 1Inline graphic4   0Inline graphic7 0Inline graphic6 0Inline graphic6   7Inline graphic3 1Inline graphic3 1Inline graphic3
Inline graphic 3Inline graphic8 1Inline graphic5 1Inline graphic5   0Inline graphic5 0Inline graphic6 0Inline graphic8   7Inline graphic6 1Inline graphic3 1Inline graphic5
Inline graphic 0Inline graphic2 0Inline graphic3 0Inline graphic3   0Inline graphic8 0Inline graphic2 0Inline graphic2   0Inline graphic5 0Inline graphic3 0Inline graphic3
Mis Inline graphic Bias ESE ASE   Bias ESE ASE   Bias ESE ASE
Inline graphic 0Inline graphic4 1e1 1e1   20 1e3 1e3   10 2e2 1e2
Inline graphic 5Inline graphic2 2e0 1e1   10 1e3 1e3   30 3e2 2e2
Inline graphic 0Inline graphic3 0Inline graphic3 0Inline graphic3   0Inline graphic8 0Inline graphic3 0Inline graphic3   0Inline graphic3 0Inline graphic5 0Inline graphic5

ESE, empirical standard error; ASE, average estimated standard error; Known Inline graphic, true propensity score known; Correct Inline graphic, propensity score unknown but correctly modelled; Mis Inline graphic, propensity score incorrectly modelled.