Maximum Pairwise Pseudo-Likelihood Estimation of the Covariance Matrix from Left-Censored Data

Michael P Jones; Sarah S Perry; Peter S Thorne

doi:10.1007/s13253-014-0185-y

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Maximum Pairwise Pseudo-Likelihood Estimation of the Covariance Matrix from Left-Censored Data

Journal article

Open access

Peer reviewed

Maximum Pairwise Pseudo-Likelihood Estimation of the Covariance Matrix from Left-Censored Data

Michael P Jones, Sarah S Perry and Peter S Thorne

Journal of agricultural, biological, and environmental statistics, Vol.20(1), pp.83-99

03/2015

DOI: 10.1007/s13253-014-0185-y

PMCID: PMC6326180

PMID: 30636858

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https://www.ncbi.nlm.nih.gov/pmc/articles/6326180View

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Abstract

Toxicological studies often depend on laboratory assays that have thresholds below which environmental pollutants cannot be measured with accuracy. Exposure levels below this limit of detection may well be toxic and hence it is vital to use data analytic methods that handle such left-censored data with as little estimation bias as possible. In an on-going study for which our methodology is developed, levels of residential exposure to polychlorinated biphenyls (PCBs) and the interrelationships of their subtypes (congeners) are characterized. In any given sample many of the congeners may fall below the detection limit. The main problem tackled in this paper is estimation of mean exposure levels and corresponding covariance and correlation matrices for a large number of potentially left-censored measures that have very low bias and are computationally feasible. The proposed methods are likelihood based, using marginal likelihoods for means and variances and pairwise pseudo-likelihoods for correlations and covariances. In the simple bi- variate case, head-to-head comparisons show the proposed methods to be computationally more stable than ordinary maximum likelihood estimates (MLEs) and still maintain comparable bias. When the number of variables is much larger than 2, the proposed methods are far more computationally feasible than MLE. Furthermore, they exhibit much less bias when compared to popular imputation procedures. Analysis of the PCB data uncovered interesting correlational structures.

Polychlorinated biphenyls

Lower detection limit

Non-detects

Principal component analysis

ISRP Project 6 2015-2020

Details

Title: Subtitle: Maximum Pairwise Pseudo-Likelihood Estimation of the Covariance Matrix from Left-Censored Data
Creators: Michael P Jones - Department of Occupational and Environmental Health University of Iowa, Iowa City, IA 52242
Sarah S Perry - Department of Occupational and Environmental Health University of Iowa, Iowa City, IA 52242
Peter S Thorne - Department of Occupational and Environmental Health University of Iowa, Iowa City, IA 52242
Resource Type: Journal article
Publication Details: Journal of agricultural, biological, and environmental statistics, Vol.20(1), pp.83-99
DOI: 10.1007/s13253-014-0185-y
PMID: 30636858
PMCID: PMC6326180
NLM abbreviation: J Agric Biol Environ Stat
ISSN: 1085-7117
eISSN: 1537-2693
Language: English
Date published: 03/2015
Academic Unit: Statistics and Actuarial Science; Civil and Environmental Engineering; Occupational and Environmental Health; Biostatistics; Public Policy Center (Archive); Iowa Superfund Research Program
Record Identifier: 9983997461302771

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