Adaptive Re-Screening and Pair-Screened Joint Rescue for Scalable Stepwise Selection in Cross-Classified Linear Mixed Models

Stepwise fixed-effect selection in complex linear mixed models is expensive because each candidate can require the re-estimation of variance components. Permanent pruning lowers this cost but can discard predictors that become relevant after other terms enter. We propose adaptive re-screened stepwise selection (ARSS), which uses a fixed-covariance generalized least-squares score to rank all remaining candidates, fully refits only a short list, and re-screens after every accepted update. We further introduce pair-screened joint rescue (ARSS-JPS) for correlated candidates that are jointly informative, although neither enters alone. A worked suppression example explains the motivation for this method. With the full covariance fixed, the scalar screening score equals the one-degree-of-freedom generalized least-squares likelihood-ratio improvement; this identity does not establish exact forward path equivalence after covariance re-estimation. In 340 known-covariance simulations, ARSS-JPS achieved a masked-scenario mean true-positive rate of 0.999 using 35.5 logical full-model fit requests versus 414.4 for exact forward selection. For an 80-dataset full-refit benchmark, it increased the masked-scenario true-positive rate from 0.768 to 0.925 and exact recovery from 0.429 to 0.600 while reducing mean full-model fit requests from 69.0 to 37.4. In the corrected reconstruction of 95,890 Polish commuting flows using orthogonal–triangular (QR) factorization, ARSS reproduced exact forward selection through the fixed-effect Stages 1–5, with 2587 rather than 62,651 logical candidate evaluations. The archived random-effect extension retained 87 fixed terms and 12 random-effect variance components.