The multivariate Poisson-log normal distribution

Aitchison, J. M.; Ho, Chih-Hsiang

doi:10.1093/biomet/76.4.643

Cited by 268 publications

(196 citation statements)

References 26 publications

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“…Bulmer (20) fitted the species abundance data, which showed that truncated, grouped LN distributions provided a satisfactory fit over the logarithmic and P-LN models, omitting zero class. Other models exist that can be useful for explaining data with a priori knowledge of the underlying distribution, such as multivariate P-LN distributions (21), bivariate Poisson distributions (19), and so on. However, LN distributions are ubiquitous and have been observed across many fields (22,23).…”

Section: Discussionmentioning

confidence: 99%

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Neti¹,

Howell²

2008

J Nucl Med

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Recently, the distribution of radioactivity among a population of cells labeled with 210 Po was shown to be well described by a lognormal (LN) distribution function (J Nucl Med. 2006;47:1049-1058 with the aid of autoradiography. To ascertain the influence of Poisson statistics on the interpretation of the autoradiographic data, the present work reports on a detailed statistical analysis of these earlier data. Methods: The measured distributions of a-particle tracks per cell were subjected to statistical tests with Poisson, LN, and Poisson-lognormal (P-LN) models. Results: The LN distribution function best describes the distribution of radioactivity among cell populations exposed to 0.52 and 3.8 kBq/mL of 210 Po-citrate. When cells were exposed to 67 kBq/mL, the P-LN distribution function gave a better fit; however, the underlying activity distribution remained lognormal. Conclusion: The present analysis generally provides further support for the use of LN distributions to describe the cellular uptake of radioactivity. Care should be exercised when analyzing autoradiographic data on activity distributions to ensure that Poisson processes do not distort the underlying LN distribution.

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Section: Discussionmentioning

confidence: 99%

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Neti¹,

Howell²

2008

J Nucl Med

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“…With the exception of Breast Cancer, these estimated correlation matrices are similar to those seen with the MCAR model, the correlation with Lung (F), Oral (F) and Oral (M) are greater in magnitude when estimated by the latent structure model, the Aitchison and Ho (1989) moment estimators are somewhere between either of these estimated. It would also appear that the main differences between these assumed correlation matrices (over which all inter-disease dependence is averaged) are in terms of the relationship between cervical cancer and Oral Cancer (M and F) as well as Lung Cancer (M).…”

Section: Latent Structure Mixture Spatial Modelmentioning

confidence: 52%

Modelling multivariate disease rates with a latent structure mixture model

Hewson

Bailey

2010

Statistical Modelling

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There has been considerable recent interest in multivariate modelling of the geographical distribution of morbidity or mortality rates for potentially related diseases. The motivations for this include: investigation of similarities or dissimilarities in the risk distribution for the different diseases, as well as 'borrowing strength' across disease rates to shrink the uncertainty in geographical risk assessment for any particular disease. A number of approaches to such multivariate modelling have been suggested and this paper proposes an extension to these which may provide a richer range of dependency structures than those encompassed so far. We develop a model which incorporates a discrete mixture of latent structures and argue that this provides potential to represent an enhanced range of correlation structures between diseases at the same time as implicitly allowing for less restrictive spatial correlation structures between geographical units. We compare and contrast our approach to other commonly used multivariate disease models and demonstrate comparative results using data taken from cancer registries on four carcinomas in some 300 geographical units in England, Scotland and Wales.

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“…The goodness of fit statistics 21 are roughly comparable for the two models. The biggest difference arises in the over dispersion statistics 22 .…”

Section: Resultsmentioning

confidence: 81%

“…Even if the covariates of the covariance structure were not significant for a specific sample in the multivariate model it would not reduce the importance of the approach. 21 The goodness of fit statistic is the scaled deviance (SAS 9.0). 22 The over dispersion statistic is the lagrange multiplier statistic from Greene [25].…”

Section: Resultsmentioning

confidence: 99%

A Multivariate Poisson Model of Consumer Choice in a Multi-Airport Region

Buck¹,

Blackstone²,

Hakim³

2009

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Using the results of a unique telephone survey the frequency of consumer flights from airports in a multi Mean usage was found to be increasing in income for PHL, but was decreasing for the other airports, reflecting the increasing value of respondents' time as their income rises. If the destination of flights is domestic (international) then the result is to increase usage of PHL, BWI and EWR (JFK). Except for JFK, if the purpose of travel is mostly pleasure then it results in more travel from JFK and less from the other three airports. The availability of a low cost carrier would result in more frequent travel.

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The multivariate Poisson-log normal distribution

Cited by 268 publications

References 26 publications

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Modelling multivariate disease rates with a latent structure mixture model

A Multivariate Poisson Model of Consumer Choice in a Multi-Airport Region

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