Saturday, January 4, 2014

The Oregon Medicaid Experiment and Linear Probability Models

I just recently discussed the methodology used in some recent papers analyzing the Oregon Medicaid expansion (see: ). This was one of the papers:

"The Oregon Experiment--Effects of Medicaid on Clinical Outcomes," by Katherine Baicker, et al. New England Journal of Medicine, 2013; 368:1713-1722. 

If you read the supplementary appendix you will find the following:

In all of our ITT estimates and in our subsequent instrumental variable estimates (see below), we fit linear models even though a number of our outcomes are binary. Because we are interested in the difference in conditional means for the treatments and controls, linear probability models would pose no concerns in the absence of covariates or in fully saturated models (Angrist 2001, Angrist and Pischke 2009). Our models are not fully saturated, however, so it is possible that results could be affected by this functional form choice, especially for outcomes with very low or very high mean probability. We therefore explore the sensitivity of our results to an alternate specification using logistic regression and calculating average marginal effects for all binary outcomes, and are reassured that the results look very similar (see Table S15a-d below). 

You will find a similar methodology in the more recent article in Science previously discussed. This weaves well with some of my past posts:

Linear Regression and Analysis of Variance with Binary Dependent Variables

Regression as an Empirical Tool (matching and linear probability models)

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