Hierarchical selection of fixed and random effects in generalized linear mixed models

    Research output: Contribution to journalArticlepeer-review

    18 Citations (Scopus)


    In many applications of generalized linear mixed models (GLMMs), there is a hierarchical structure in the effects that needs to be taken into account when performing variable selection. A prime example of this is when fitting mixed models to longitudinal data, where it is usual for covariates to be included as only fixed effects or as composite (fixed and random) effects. In this article, we propose the first regularization method that can deal with large numbers of candidate GLMMs while preserving this hierarchical structure: CREPE (Composite Random Effects PEnalty) for joint selection in mixed models. CREPE induces sparsity in a hierarchical manner, as the fixed effect for a covariate is shrunk to zero only if the corresponding random effect is or has already been shrunk to zero. In the setting where the number of fixed effects grow at a slower rate than the number of clusters, we show that CREPE is selection consistent for both fixed and random effects, and attains the oracle property. Simulations show that CREPE outperforms some currently available penalized methods for mixed models.

    Original languageEnglish
    Pages (from-to)501-518
    Number of pages18
    JournalStatistica Sinica
    Issue number2
    Publication statusPublished - Apr 2017


    Dive into the research topics of 'Hierarchical selection of fixed and random effects in generalized linear mixed models'. Together they form a unique fingerprint.

    Cite this