Likelihood-based and Bayesian methods for Tweedie compound Poisson linear mixed models

Zhang, Yanwei

doi:10.1007/s11222-012-9343-7

Cited by 157 publications

(155 citation statements)

References 28 publications

Supporting

Mentioning

155

Contrasting

Order By: Relevance

“…Other data including speeds and durations were treated as Gaussian, and log transformed when plots of residuals indicated a violation of the assumption of equal variance. Scaled effort data were continuous and zero-inflated and thus we employed a compound Poisson linear mixed model using the cplm package in R [52]. In analyses of speed, individual identity was added as a nested random factor within colony.…”

Section: Discussionmentioning

confidence: 99%

Ants work harder during consensus decision-making in small groups

Cronin

Stumpe²

2014

J. R. Soc. Interface.

View full text Add to dashboard Cite

Individuals derive many benefits from being social, one of which is improved accuracy of decision-making, the so-called 'wisdom of the crowds' effect. This advantage arises because larger groups can pool information from more individuals. At present, limited empirical data indicate that larger groups outperform smaller ones during consensus decision-making in human and non-human animals. Inaccurate decisions can lead to significant costs, and we might therefore expect individuals in small groups to employ mechanisms to compensate for the lack of numbers. Small groups may be able to maintain decision accuracy if individuals are better informed than those in larger groups and/or by increasing the proportion of the group involved in collective decision-making relative to larger groups. In this study, we use interactive computer vision software to investigate individual contributions to consensus decision-making during house-hunting in different sized groups of the ant Myrmecina nipponica. We show that individuals in small colonies invest greater effort in the consensus decision process than those in large colonies and should be better informed as a result. This may act to ameliorate the limitations of group size, but could leave smaller groups more susceptible to additional stresses.

show abstract

Section: Discussionmentioning

confidence: 99%

Ants work harder during consensus decision-making in small groups

Cronin

Stumpe²

2014

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…Although the theory of the Tweedie families has been known for more than 20 years, only recently have software packages that allow easy handling of these distributions become available [16, 23]. Further research should explore the usefulness of Tweedie distributions with p >2 as they provide similar shape to the Gamma but support heavier tails.…”

Section: Discussionmentioning

confidence: 99%

“…Recovering the underlying marginal distribution of Z results in a non-closed form expression for the normalizing function a (·), based on Wright’s generalized Bessel function W (·,·,·) [13, 16]: …”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Tweedie distributions for fitting semicontinuous health care utilization cost data

Kurz

2017

BMC Med Res Methodol

View full text Add to dashboard Cite

Background: The statistical analysis of health care cost data is often problematic because these data are usually non-negative, right-skewed and have excess zeros for non-users. This prevents the use of linear models based on the Gaussian or Gamma distribution. A common way to counter this is the use of Two-part or Tobit models, which makes interpretation of the results more difficult. In this study, I explore a statistical distribution from the Tweedie family of distributions that can simultaneously model the probability of zero outcome, i.e. of being a non-user of health care utilization and continuous costs for users. Methods: I assess the usefulness of the Tweedie model in a Monte Carlo simulation study that addresses two common situations of low and high correlation of the users and the non-users of health care utilization. Furthermore, I compare the Tweedie model with several other models using a real data set from the RAND health insurance experiment. Results: I show that the Tweedie distribution fits cost data very well and provides better fit, especially when the number of non-users is low and the correlation between users and non-users is high. Conclusion:The Tweedie distribution provides an interesting solution to many statistical problems in health economic analyses.

show abstract

“…It is known that the index parameter β affects the robustness of parameter estimation (Cichocki and Amari, 2010). Although there are several approaches to determining the value of β (Zhang, 2013), it is a considerably difficult and complicated problem, and selecting an error distribution in NMF is often based on prior knowledge about the given data. For example, for count data, it is appropriate to use a Poisson distribution as the error distribution.…”

Section: Introductionmentioning

confidence: 99%

Automatic Relevance Determination in Nonnegative Matrix Factorization Based on a Zero-Inflated Compound Poisson-Gamma Distribution

Abe

Yadohisa

2016

Journal of the Japanese Society of Computational Statistics

View full text Add to dashboard Cite

In this paper, we consider the determination of the number of factors in nonnegative matrix factorization (NMF) for a zero-inflated data matrix. This zero-inflated case leads to poor approximation to the nonnegative data matrix. To address this problem, we use the zero-inflated compound Poisson-gamma distribution as the error distribution in NMF. In addition, we consider automatic relevance determination (ARD) for model order selection. Our simulation study shows that our method is better than the basic ARD method for zero-inflated data. We apply our proposed method to real-world purchasing data to determine the number of buying patterns.

show abstract

Likelihood-based and Bayesian methods for Tweedie compound Poisson linear mixed models

Cited by 157 publications

References 28 publications

Ants work harder during consensus decision-making in small groups

Ants work harder during consensus decision-making in small groups

Tweedie distributions for fitting semicontinuous health care utilization cost data

Automatic Relevance Determination in Nonnegative Matrix Factorization Based on a Zero-Inflated Compound Poisson-Gamma Distribution

Contact Info

Product

Resources

About