Exact Calculation of Coefficient of Proportionality Including Evaluation of Oster's [Delta]*, Corresponding Bounds, and Alternatives

Autor/inn/en	Frank, Kenneth A.; Lin, Qinyun; Maroulis, Spiro
Titel	*Exact Calculation of Coefficient of Proportionality Including Evaluation of Oster's [Delta], Corresponding Bounds, and Alternatives**
Quelle	(2023), (60 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Frank, Kenneth A.) Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
DOI	10.2139/ssrn.4305243
Schlagwörter	Computation; Statistical Analysis; Statistical Inference; Correlation; Accuracy; Sample Size; Best Practices; Equations (Mathematics) + Suchen Sie Ihr Suchwort? Statistische Analyse; Inferential statistics; Schließende Statistik; Korrelation; Equations; Mathematics; Gleichungslehre
Abstract	Beginning with debates about the effects of smoking on lung cancer, sensitivity analyses characterizing the hypothetical unobserved conditions that can alter statistical inferences have had profound impacts on public policy. One of the most ascendant techniques for sensitivity analysis is Oster's (2019) coefficient of proportionality, which approximates how strong selection into a treatment on unobserved variables must be compared to selection on observed variables to change an inference. We refine Oster's asymptotic approximation by deriving expressions for the correlations associated with a latent omitted variable that reduce an estimated effect to a specified threshold, given a corresponding coefficient of determination (R[superscript 2]). We verify our expressions through empirical examples and simulated data. We show that, because our calculations are exact, they apply regardless of sample size. In contrast, Oster's approximation is likely to overstate robustness when sample size is small and observed covariates account for a large portion of an estimated effect relative to a baseline model. Moreover, even in cases that produce similar values, our correlation-based expressions have the advantage of not depending on the analyst's choice of a baseline model. Our correlation-based expressions can be directly calculated from conventionally reported quantities through commands in R or Stata and an on-line app, and therefore can be applied to most published studies. We present best practices including making maximal use of observed covariates, caution (and an alternative correlation metric) when selection on observables is small and considering a minimum value of the maximal variance to be explained. [Cowritten with Shimeng Dai, Nicole Jess, Hung-Chang Lin, Yuqing Liu, Sarah Maestrales, Ellen Searle, and Jordan Tait. This paper will be published.] (As Provided).
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01