Causal Inference and Robustness Indices

Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to Change an Inference?: Using Rubin’s Causal Model to Interpret the Robustness of Causal Inferences. Education, Evaluation and Policy Analysis. Vol 35: 437-460.

PPT presentation

Frank, K.A., Gary Sykes, Dorothea Anagnostopoulos, Marisa Cannata, Linda Chard, Ann Krause, Raven McCrory. 2008. Extended Influence: National Board Certified Teachers as Help Providers. Education, Evaluation, and Policy Analysis. Vol 30(1): 3-30.

*Frank, K. A. and Min, K. 2007. Indices of Robustness for Sample Representation. Sociological Methodology. Vol 37, 349-392. * co first authors.

Frank, K. 2000. "Impact of a Confounding Variable on the Inference of a Regression Coefficient." Sociological Methods and Research, 29(2), 147-194

The Impact of a Confounding Variable on a Regression Coefficient

When one reports a regression from an observational study, there is always the concern: "But have you controlled for xxx?" In this article, I index the impact of a confounding variable in terms of the product of two correlations (correlation between the confounding variable and the predictor of interest X correlation between the confounding variable and the outcome -- see figure below). This product appears in both the estimate of a regression coefficient and its standard error. Thus it can be used to quantify the impact necessary to alter a statistical inference. In the article I develop the index for the bivariate and multivariate contexts, compare it to other statistics, apply to an example, describe a reference distribution, and then interpret in the context of recent concerns about causal and statistical inferences.