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A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. What are the conditions of validity that are needed to apply a "robust error variance Poisson regression"? Or in other words, are there any number of assumptions that must be met before doing such a model?

References:

Guangyong Zou, A Modified Poisson Regression Approach to Prospective Studies with Binary Data, Am. J. Epidemiol. (2004) 159 (7): 702-706 doi:10.1093/aje/kwh090

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    $\begingroup$ Can you clarify the situation that lies behind your question? In what sense do you mean "validity"? What specific model do you mean by "robust error variance Poisson regression"? $\endgroup$ – gung - Reinstate Monica Sep 7 '16 at 16:36
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There is a useful discussion by Lumley and colleagues "Relative risk regression in medical research: models, contrasts, estimators, and algorithms" available here which despite the title is not exclusive to medical research.

As I understand it the main problem with the Poisson working model is that it is capable of giving predicted probabilities greater than 1. The other main competitor, the log-binomial does not do that. Whether you see this as a problem with the algorithm or a problem with using relative risks where the baseline risk is high is a matter for your decision I think.

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To add to @mdewey's answer

The issue with maximum likelihood is that it constrains fitted probabilities to be at most 1, which can give x-outliers extremely high influence on the results. As a consequence, the estimator takes some effort to compute reliably, and its distribution might not be close to Normal

Any estimator that avoids the outlier-sensitivity of the MLE must do so by allowing fitted probabilities greater than 1, as the Poisson working model does. Reasonable people can disagree on whether that's a good tradeoff.

One important reason for picking the Poisson working model over other alternatives to the MLE (such as nonlinear least squares) is partly aesthetic: it approximates the MLE well when the fitted probabilities are small. This allows the same estimator to be used for rare and common events.

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