Missing covariate data in generalized linear mixed models with distribution-free random effects
We consider generalized linear mixed models in which random effects are free of parametric distributions and missing at random data are present in some covariates. To overcome the problem of missing data, we propose two novel methods relying on auxiliary variables: a penalized conditional likelihood...
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2019
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| Online Access: | https://hdl.handle.net/10356/105576 http://hdl.handle.net/10220/50235 |
| _version_ | 1826120491824316416 |
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| author | Liu, Li Xiang, Liming |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Liu, Li Xiang, Liming |
| author_sort | Liu, Li |
| collection | NTU |
| description | We consider generalized linear mixed models in which random effects are free of parametric distributions and missing at random data are present in some covariates. To overcome the problem of missing data, we propose two novel methods relying on auxiliary variables: a penalized conditional likelihood method when covariates are independent of random effects, and a two-step procedure consisting of a pairwise likelihood for estimating fixed effects in the first step and a penalized conditional likelihood for estimating random effects in the second step while covariates can be related to random effects. Our methods allow a nonparametric structure for the missing covariate data and do not rely on distribution assumptions for random effects, which are not observed in the data, thus providing great flexibility in capturing a board range of the missingness mechanism and behaviors of random effects. We show that the proposed estimators enjoy desirable theoretical properties by relaxing the conditions for a finite number of clusters or finite cluster size imposed in the literature. The finite sample performance of the estimators is assessed through extensive simulations. We illustrate the application of the methods using a longitudinal data set on forest health monitoring. |
| first_indexed | 2024-10-01T05:17:20Z |
| format | Journal Article |
| id | ntu-10356/105576 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:17:20Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/1055762023-02-28T19:44:10Z Missing covariate data in generalized linear mixed models with distribution-free random effects Liu, Li Xiang, Liming School of Physical and Mathematical Sciences Generalized Linear Mixed Model Auxiliary Variable Science::Mathematics We consider generalized linear mixed models in which random effects are free of parametric distributions and missing at random data are present in some covariates. To overcome the problem of missing data, we propose two novel methods relying on auxiliary variables: a penalized conditional likelihood method when covariates are independent of random effects, and a two-step procedure consisting of a pairwise likelihood for estimating fixed effects in the first step and a penalized conditional likelihood for estimating random effects in the second step while covariates can be related to random effects. Our methods allow a nonparametric structure for the missing covariate data and do not rely on distribution assumptions for random effects, which are not observed in the data, thus providing great flexibility in capturing a board range of the missingness mechanism and behaviors of random effects. We show that the proposed estimators enjoy desirable theoretical properties by relaxing the conditions for a finite number of clusters or finite cluster size imposed in the literature. The finite sample performance of the estimators is assessed through extensive simulations. We illustrate the application of the methods using a longitudinal data set on forest health monitoring. MOE (Min. of Education, S’pore) Accepted version 2019-10-23T04:46:56Z 2019-12-06T21:53:49Z 2019-10-23T04:46:56Z 2019-12-06T21:53:49Z 2018 Journal Article Liu, L., & Xiang, L. (2019). Missing covariate data in generalized linear mixed models with distribution-free random effects. Computational Statistics & Data Analysis, 134, 1-16. doi:10.1016/j.csda.2018.10.011 0167-9473 https://hdl.handle.net/10356/105576 http://hdl.handle.net/10220/50235 10.1016/j.csda.2018.10.011 en Computational Statistics & Data Analysis © 2018 Elsevier B.V. All rights reserved. This paper was published in Computational Statistics & Data Analysis and is made available with permission of Elsevier B.V. 35 p. application/pdf |
| spellingShingle | Generalized Linear Mixed Model Auxiliary Variable Science::Mathematics Liu, Li Xiang, Liming Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title | Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title_full | Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title_fullStr | Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title_full_unstemmed | Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title_short | Missing covariate data in generalized linear mixed models with distribution-free random effects |
| title_sort | missing covariate data in generalized linear mixed models with distribution free random effects |
| topic | Generalized Linear Mixed Model Auxiliary Variable Science::Mathematics |
| url | https://hdl.handle.net/10356/105576 http://hdl.handle.net/10220/50235 |
| work_keys_str_mv | AT liuli missingcovariatedataingeneralizedlinearmixedmodelswithdistributionfreerandomeffects AT xiangliming missingcovariatedataingeneralizedlinearmixedmodelswithdistributionfreerandomeffects |