Valid Inference after Model Selection and the selectiveInference Package

Since model selection methods choose the "best" model in some sense, significance tests for variables in that model will tend to be anti-conservative, and goodness of fit tests will tend to be conservative. This is troubling, as it implies these tests in practice do not actually provide evidence in favor of the chosen variables or model. We demonstrate methods of post-selection inference to obtain conditionally valid significance tests and conditionally unbiased goodness of fit tests and show how these outperform unadjusted tests.