Testing assumptions and counterfactuals

The following are materials related to my research on testing assumptions in statistical models.

Evaluating the Consequences of Assumptions Using Simulations
The Political Methodologist, 11(1):21--25

While prominent in some aspects of statistical analysis, simulations are infrequently used to evaluate the quality of specific empirical statistical results. Since few researchers would argue that they have a perfectly specified model, how much we believe a particular set of results depends on the degree to which assumptions of the statistical model are believed to be violated and the robustness of the model to those violations. Although assumptions will in general be unverifiable, the value of a particular empirical analysis can be made clearer by characterizing how inference would change if the assumptions did not hold. Two useful criteria for evaluating the sensitivity of models can be provided using simulations. First, the degree of assumption violation necessary to change our beliefs about competing theories, such as causing the false rejection of a hypothesis. Second, at what point would it no longer be possible to recover the results originally found using the actual data.