NDLI: Maximum likelihood estimation of regression parameters with spatially dependent discrete data

Content Provider	Springer Nature Link
Author	Madsen, L.
Copyright Year	2009
Abstract	Generalized estimating equations (GEEs) have been successfully used to estimate regression parameters from discrete longitudinal data. GEEs have been adapted for spatially correlated count data with less success. It is convenient to model correlated counts as lognormal-Poisson, where a latent lognormal random process carries all correlation. This model limits correlation and can lead to negative bias of standard errors. Moreover, correlation is not the best dependence measure for highly nonnormal data. This article proposes a model which yields maximum likelihood (ML) estimates of regression parameters when the response is discrete and spatially dependent. This model employs a spatial Gaussian copula, bringing the discrete distribution into the Gaussian geostatistical framework, where correlation completely describes dependence. The model yields a log-likelihood for regression parameters that can be maximized using established numerical methods. The proposed procedure is used to estimate the relationship between Japanese beetle grub counts and soil organic matter. These data exhibit residual correlation well above the lognormal-Poisson correlation limit, so that model is not appropriate. The data and MATLAB code are available online. Simulations demonstrate that negative bias in GEE standard errors leads to nominal 95% confidence coverage less than 62% for moderate or strong spatial dependence, whereas ML coverage remains above 82%.
Starting Page	375
Ending Page	391
Page Count	17
File Format	PDF
ISSN	10857117
Journal	Journal of Agricultural, Biological, and Environmental Statistics
Volume Number	14
Issue Number	4
e-ISSN	15372693
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Continuous extension Correlated count data Dependent count data Gaussian copula Spatial copula Statistics for Life Sciences, Medicine, Health Sciences Agriculture Environmental Monitoring/Analysis Biostatistics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Environmental Science Agricultural and Biological Sciences Statistics, Probability and Uncertainty

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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