A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

Yawen Guan, Murali Haran

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduced-dimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction; our methods also compare favorably to existing “reduced-rank” approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types. Supplementary material for this article is available online.

Original languageEnglish (US)
Pages (from-to)701-714
Number of pages14
JournalJournal of Computational and Graphical Statistics
Volume27
Issue number4
DOIs
StatePublished - Oct 2 2018

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Generalized Linear Mixed Model
High-dimensional
Markov Chain Monte Carlo Algorithms
Confounding
Projection
Random Effects
Reduced Rank
Random Projection
Coefficient Estimates
Regression Estimate
Fixed Effects
Count Data
Spatial Data
Bayesian inference
Regression Coefficient
Speedup
Tend
Iteration
Prediction
Generalized linear mixed model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

Cite this

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A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models. / Guan, Yawen; Haran, Murali.

In: Journal of Computational and Graphical Statistics, Vol. 27, No. 4, 02.10.2018, p. 701-714.

Research output: Contribution to journalArticle

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