zeta

Of limited interest to most users, the zeta function plays an internal role in 2-sample and stratified sensitivity analyses. The zeta function is equation (8), page 495, in Rosenbaum and Krieger (1990).

Supplements for a book, "iTOS" = "Introduction to the Theory of Observational Studies." Data sets are 'aHDL' from Rosenbaum (2023a) <doi:10.1111/biom.13558> and 'bingeM' from Rosenbaum (2023b) <doi:10.1111/biom.13921>. The function makematch() uses two-criteria matching from Zhang et al. (2023) <doi:10.1080/01621459.2021.1981337> to create the matched data 'bingeM' from 'binge'. The makematch() function also implements optimal matching (Rosenbaum (1989) <doi:10.2307/2290079>) and matching with fine or near-fine balance (Rosenbaum et al. (2007) <doi:10.1198/016214506000001059> and Yang et al (2012) <doi:10.1111/j.1541-0420.2011.01691.x>). The book makes use of two other R packages, 'weightedRank' and 'tightenBlock'.

Paul Rosenbaum

iTOS

Methods and Examples from Introduction to the Theory of
Observational Studies

zeta function

<dl> <dt>bigN</dt>
<dd>Total sample size in this stratum.</dd> <dt>n</dt>
<dd>Treated sample size in this stratum.</dd> <dt>m</dt>
<dd>The number of 1's in the vector u of unobserved covariates. Here, u
has bigN-m 0's followed by m 1's.</dd> <dt>g</dt>
<dd>The sensitivity parameter \(\Gamma\), where \(\Gamma \ge 1\).</dd></dl>

Arguments

Author

zeta function in sensitivity analysis — zeta

<dl>

 <dt>bigN</dt>
<dd>Total sample size in this stratum.</dd>

 <dt>n</dt>
<dd>Treated sample size in this stratum.</dd>

 <dt>m</dt>
<dd>The number of 1's in the vector u of unobserved covariates. Here, u
has bigN-m 0's followed by m 1's.</dd>

 <dt>g</dt>
<dd>The sensitivity parameter \(\Gamma\), where \(\Gamma \ge 1\).</dd>

</dl>

zeta: zeta function in sensitivity analysis

Description

Usage

Value

Arguments

Author

References

Examples