Statistical significance in high-dimensional linear mixed models
This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have repeated measurements for subjects. We consider a scenario where the number of fixed effects is large (and may be larger than ), but...
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| Vydané v: | FODS '20 : proceedings of the 2020 ACM-IMS Foundations of Data Science Conference : October 19-20, 2020, Virtual Event, USA. ACM-IMS Foundations of Data Science Conference (2020 : Online) Ročník 2020; s. 171 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
01.10.2020
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| Abstract | This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have
repeated measurements for
subjects. We consider a scenario where the number of fixed effects
is large (and may be larger than
), but the number of random effects
is small. Our framework is inspired by a recent line of work that proposes de-biasing penalized estimators to perform inference for high-dimensional linear models with fixed effects only. In particular, we demonstrate how to correct a 'naive' ridge estimator in extension of work by Bühlmann (2013) to build asymptotically valid confidence intervals for mixed effect models. We validate our theoretical results with numerical experiments, in which we show our method outperforms those that fail to account for correlation induced by the random effects. For a practical demonstration we consider a riboflavin production dataset that exhibits group structure, and show that conclusions drawn using our method are consistent with those obtained on a similar dataset without group structure. |
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| AbstractList | This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have
repeated measurements for
subjects. We consider a scenario where the number of fixed effects
is large (and may be larger than
), but the number of random effects
is small. Our framework is inspired by a recent line of work that proposes de-biasing penalized estimators to perform inference for high-dimensional linear models with fixed effects only. In particular, we demonstrate how to correct a 'naive' ridge estimator in extension of work by Bühlmann (2013) to build asymptotically valid confidence intervals for mixed effect models. We validate our theoretical results with numerical experiments, in which we show our method outperforms those that fail to account for correlation induced by the random effects. For a practical demonstration we consider a riboflavin production dataset that exhibits group structure, and show that conclusions drawn using our method are consistent with those obtained on a similar dataset without group structure. This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have n repeated measurements for M subjects. We consider a scenario where the number of fixed effects p is large (and may be larger than M), but the number of random effects q is small. Our framework is inspired by a recent line of work that proposes de-biasing penalized estimators to perform inference for high-dimensional linear models with fixed effects only. In particular, we demonstrate how to correct a 'naive' ridge estimator in extension of work by Bühlmann (2013) to build asymptotically valid confidence intervals for mixed effect models. We validate our theoretical results with numerical experiments, in which we show our method outperforms those that fail to account for correlation induced by the random effects. For a practical demonstration we consider a riboflavin production dataset that exhibits group structure, and show that conclusions drawn using our method are consistent with those obtained on a similar dataset without group structure.This paper concerns the development of an inferential framework for high-dimensional linear mixed effect models. These are suitable models, for instance, when we have n repeated measurements for M subjects. We consider a scenario where the number of fixed effects p is large (and may be larger than M), but the number of random effects q is small. Our framework is inspired by a recent line of work that proposes de-biasing penalized estimators to perform inference for high-dimensional linear models with fixed effects only. In particular, we demonstrate how to correct a 'naive' ridge estimator in extension of work by Bühlmann (2013) to build asymptotically valid confidence intervals for mixed effect models. We validate our theoretical results with numerical experiments, in which we show our method outperforms those that fail to account for correlation induced by the random effects. For a practical demonstration we consider a riboflavin production dataset that exhibits group structure, and show that conclusions drawn using our method are consistent with those obtained on a similar dataset without group structure. |
| Author | Drton, Mathias Shojaie, Ali Lin, Lina |
| Author_xml | – sequence: 1 givenname: Lina surname: Lin fullname: Lin, Lina organization: Department of Statistics, University of Washington – sequence: 2 givenname: Mathias surname: Drton fullname: Drton, Mathias organization: Department of Mathematics, Technical University of Munich – sequence: 3 givenname: Ali surname: Shojaie fullname: Shojaie, Ali organization: Department of Biostatistics, University of Washington |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/35497571$$D View this record in MEDLINE/PubMed |
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| Title | Statistical significance in high-dimensional linear mixed models |
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