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Generalized linear models (GLMs) are popular for data-analysis in almost allquantitative sciences, but the choice of likelihood family and link function isoften difficult. This motivates the search for likelihoods and links thatminimize the impact of potential misspecification. We perform a large-scalesimulation study on double-bounded and lower-bounded response data where wesystematically vary both true and assumed likelihoods and links. In contrast toprevious studies, we also study posterior calibration and uncertainty metricsin addition to point-estimate accuracy. Our results indicate that certainlikelihoods and links can be remarkably robust to misspecification, performingalmost on par with their respective true counterparts. Additionally, normallikelihood models with identity link (i.e., linear regression) often achievecalibration comparable to the more structurally faithful alternatives, at leastin the studied scenarios. On the basis of our findings, we provide practicalsuggestions for robust likelihood and link choices in GLMs.

Posterior accuracy and calibration under misspecification in Bayesian generalized linear models