Post-Selection Inference for Multiverse Analysis in Mixed-Effects Models (PIMAX)

Sign-flipping score tests provide robust inference in generalized linear models under variance misspecification and form the basis of two recently proposed inferential frameworks: Post-selection Inference in Multiverse Analysis (PIMA) and the flip2sss two-stage summary statistics approach. PIMA enables valid inference across a multiverse of model specifications with asymptotic control of the family-wise error rate, whereas flip2sss extends the resampling-based score test to longitudinal and hierarchical data settings. In this paper, we unify these two frameworks by extending multiverse inference to contexts involving dependent observations. Heteroscedasticity, unbalanced designs, and within-cluster dependence are accommodated nonparametrically, without requiring specification of a random-effects correlation structure, as is typically assumed in conventional generalized linear mixed models.