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On Poisson-exponential-Tweedie models for ultra-overdispersed count data

ASTA-ADVANCES IN STATISTICAL ANALYSIS 2021年第1期105卷 1-23页

作者： Abid, Rahma Kokonendji, Celestin C. Masmoudi, Afif Univ Sfax Lab Probabil & Stat Sfax Tunisia Paris Dauphine Univ Tunis Tunis Tunisia Univ Bourgogne Franche Comte Lab Math Besancon Besancon France

We introduce a new class of Poisson-exponential-Tweedie (PET) mixture in the framework of generalized linear models for ultra-overdispersed count data. The mean-variance relationship is of the form m + m(2) + phi m(p), where phi and pare the dispersion and Tweedie power parameters, respectively. The proposed model is equivalent to the exponential-Poisson-Tweedie models arising from geometric sums of Poisson-Tweedie random variables. In this respect, the PET models encompass the geometric versions of Hermite, Neyman Type A, Polya-Aeppli, negative binomial and Poisson-inverse Gaussian models. The algorithms we shall propose allow to estimate the real power parameter, which works as an automatic distribution selection. Instead of the classical Poisson, zero-shifted geometric is presented as the reference count distribution. Practical properties are incorporated into the PET of new relative indexes of dispersion and zero-inflation phenomena. Simulation studies demonstrate that the proposed model highlights unbiased and consistent estimators for large samples. Illustrative practical applications are analysed on count data sets, in particular, PET models for data without covariates and PET regression models. The PET models are compared to Poisson-Tweedie models showing that parameters of both models are adopted to data.

关键词： generalized linear models Geometric dispersion models Quasi-likelihood Relative dispersion index Relative zero inflation

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Efficient Likelihood Estimation of generalized Structural Equation models with a Mix of Normal and Nonnormal Responses

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PSYCHOMETRIKA 2021年第2期86卷 642-667页

作者： Rockwood, Nicholas J. Loma Linda Univ Loma Linda CA 92350 USA

A maximum likelihood estimation routine is presented for a generalized structural equation model that permits a combination of response variables from various distributions (e.g., normal, Poisson, binomial, etc.). The likelihood function does not have a closed-form solution and so must be numerically approximated, which can be computationally demanding for models with several latent variables. However, the dimension of numerical integration can be reduced if one or more of the latent variables do not directly affect any nonnormal endogenous variables. The method is demonstrated using an empirical example, and the full estimation details, including first-order derivatives of the likelihood function, are provided.

关键词： structural equation modeling latent variable modeling generalized linear models maximum likelihood estimation

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Population status and factors influencing the distribution of Critically Endangered gharial (Gavialis gangeticus) in a regulated unprotected river system in India

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GLOBAL ECOLOGY AND CONSERVATION 2023年 46卷

作者： Panda, Ashish Kumar Katdare, Suyash Gawan, Saurav Sharma, Surya Prasad Badola, Ruchi Hussain, Syed Ainul Wildlife Inst India Ganga Aqualife Conservat & Monitoring Ctr POB 18 Dehra Dun 248001 Uttarakhand India

Gharial (Gavialis gangeticus), the last surviving crocodilian member of the genus Gavialis, is endemic to the Indian subcontinent and is listed as one of the priorities species under the Evolutionary Distinct and Globally Endangered framework. Historically, the gharial used to occur in all major river systems of the Indian Subcontinent, now found in isolated stretches, mostly within the boundaries of Protected Areas. The gharial population decreased by over 80 % between the 1950s and 1960s due to habitat degradation, poaching, and mortality from passive fishing. The gharial population is, however, rebounding due to concerted conservation efforts launched in the mid-1970s. One of the largest gharial populations outside of the Protected Area is in the Gandak River, a transboundary northern tributary of the Ganga. However, the habitat association of gharial in relation to the rising anthropogenic stressors is not well-documented from an ecological standpoint in the Gandak River. The present study assessed the population status and factors influencing the gharial distribution in the Gandak River. Boat-based visual encounter surveys were conducted for data collection, and generalized linear models (GLMs) were employed to evaluate the factors influencing gharial distribution. The encounter rate fluctuated along the surveyed river stretches, peaking in the upstream. We observed a positive association with channel depth while a negative one with channel width, livestock presence, fishing nets, and fishing boats. The observed pattern of encounter rate and negative association with anthropogenic variables indicate spatial avoidance of these factors. Overall, conservation interventions, such as adaptive management strategies to reduce and remove these factors, are required for longterm gharial persistence in the regulated unprotected riverscape.

关键词： Size-class composition Habitat use Riverscape Anthropogenic threats generalized linear models Crocodile

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Comparison of various models for the estimation of heritability and breeding values

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TROPICAL ANIMAL HEALTH AND PRODUCTION 2023年第4期55卷 250-250页

作者： Hamadani, Ambreen Ganai, Nazir. A. A. Khan, Nusrat Nabi Shanaz, Syed Rather, Mubashir Ali Ahmad, Haider. A. A. Shah, Ruksana Sher Ekashmir Univ Agr Sci & Technol Kashmir Srinagar 190025 Jammu & Kashmir India Natl Inst Technol Srinagar 190008 Jammu & Kashmir India Dept Sheep Husb Kashmir Jammu & Kashmir India

The exploration of additive genetic variance for the selection of animals is the central paradigm in quantitative genetics and it is important to use appropriate animal models considering important factors. This study compares various factor effects for heritability and breeding values estimations on data collected on the Corriedale. Overall, the heritability estimates were the highest for birthweight (BW). Both the additive genetic variance and the heritability values were reduced upon adding more random effects. Year-effect as random reduced the heritability except for BW. The highest average accuracy for breeding values for birth, weaning, 6, 9, and 12-month-weights for were 0.656, 0.567, 0.519, 0.486, and 0.515. These were observed for models having sex or sex and parity as fixed effects. It is concluded that fixed and random factors have a significant impact on genetic-factors and breeding-value accuracies and should be considered during selection programs and make the selection program more effective.

关键词： Heritability Animal models generalized linear models Bayesian models

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Examination of the Effect of Task Complexity and Coping Capacity on Driving Risk: A Cross-Country and Transportation Mode Comparative Study

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SENSORS 2023年第24期23卷 9663-9663页

作者： Roussou, Stella Garefalakis, Thodoris Michelaraki, Eva Katrakazas, Christos Adnan, Muhammad Khattak, Muhammad Wisal Brijs, Tom Yannis, George Natl Tech Univ Athens Dept Transportat Planning & Engn 5 Iroon Polytech Str Athens 15773 Greece Hasselt Univ Transportat Res Inst IMOB Sch Transportat Sci B-3500 Hasselt Belgium

The i-DREAMS project established a 'Safety Tolerance Zone (STZ)' to maintain operators within safe boundaries through real-time and post-trip interventions, based on the crucial role of the human element in driving behavior. This paper aims to model the inter-relationship among driving task complexity, operator and vehicle coping capacity, and crash risk. Towards that aim, data from 80 drivers, who participated in a naturalistic driving experiment carried out in three countries (i.e., Belgium, Germany, and Portugal), resulting in a dataset of approximately 19,000 trips were collected and analyzed. The exploratory analysis included the development of generalized linear models (GLMs) and the choice of the most appropriate variables associated with the latent variables "task complexity" and "coping capacity" that are to be estimated from the various indicators. In addition, Structural Equation models (SEMs) were used to explore how the model variables were interrelated, allowing for both direct and indirect relationships to be modeled. Comparisons on the performance of such models, as well as a discussion on behaviors and driving patterns across different countries and transport modes, were also provided. The findings revealed a positive relationship between task complexity and coping capacity, indicating that as the difficulty of the driving task increased, the driver's coping capacity increased accordingly, (i.e., higher ability to manage and adapt to the challenges posed by more complex tasks). The integrated treatment of task complexity, coping capacity, and risk can improve the behavior and safety of all travelers, through the unobtrusive and seamless monitoring of behavior. Thus, authorities should utilize a data system oriented towards collecting key driving insights on population level to plan mobility and safety interventions, develop incentives for road users, optimize enforcement, and enhance community building for safe traveling.

关键词： task complexity coping capacity crash risk generalized linear models structural equation models

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Climate-Growth Relationships in Laurus azorica-A Dominant Tree in the Azorean Laurel Forest

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FORESTS 2023年第2期14卷 166页

作者： Pavao, Diogo C. Jevsenak, Jernej Silva, Lurdes Borges Elias, Rui Bento Silva, Luis Univ Acores Ctr Invest Biodiversidade & Recursos Genet InBIO Lab Associado CIBIOPolo Acores Campus Ponta DelgadaRua Mae Deus P-9500321 Ponta Delgada Portugal Univ Azores Fac Sci & Technol Campus Ponta DelgadaRua Mae Deus P-9500321 Ponta Delgada Portugal CIBIO BIOPOLIS Program Genom Biodivers & Land Planning Campus Vairao P-4485661 Vairao Portugal UNESCO Chair Land Sea Biodivers & Sustainabil Atl London England Tech Univ Munich TUM Sch Life Sci D-85354 Freising Weihenstephan Germany Slovenian Forestry Inst Dept Forest & Landscape Planning & Monitoring Ljubljana 1000 Slovenia Univ Azores CHANGE Global Change & Sustainabil Inst CE3c Ctr Ecol Evolut & Environm Changes Fac Agr & Environm SciAzorean Biodiversity Grp Rua Capitao Joao Avila P-9700042 Pico Da Urze Angra Do Herois Portugal

Forests on oceanic islands, such as the Azores archipelago, enable interesting dendroclimatic research, given their pronounced climatic gradients over short geographical distances, despite the less pronounced seasonality. The Lauraceae play an essential ecological role in Macaronesian natural forests. An example is Laurus azorica (Seub.) Franco, a relevant species given its high frequency and physiognomic dominance in Azorean laurel forests. This study aims to quantify climate-growth relationships in L. azorica using a dendroecological approach. We sampled four stands at Sao Miguel and two stands at Terceira islands, for a total of 206 trees. Following standard dendrochronological methods and rigorous sample selection procedures, we obtained relatively low rbar values and high temporal autocorrelation. Using a stepwise Random Forest analysis followed by generalized linear models calculation, we found prominent effects of present and previous year temperature, but a low precipitation signal on growth rings, with some model variation between stands. Our results agreed with previous observations for broad-leaved species with diffuse porous wood, contributing to increase the baseline dendroecological knowledge about Azorean forests. Due to the high levels of within- and between-stand variation, and to refine the climatic signal analysis, complementary approaches should be explored in the future.

关键词： Azores dendroclimatology generalized linear models laurel forest Macaronesia random forest

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generalized symmetrical partial linear model

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JOURNAL OF APPLIED STATISTICS 2021年第3期48卷 557-572页

作者： Souza Vasconcelos, Julio Cezar Villegas, Cristian Univ Sao Paulo Piracicaba Brazil

In this work, we propose a new model called generalized symmetrical partial linear model, based on the theory of generalized linear models and symmetrical distributions. In our model the response variable follows a symmetrical distribution such a normal, Student-t, power exponential, among others. Following the context of generalized linear models we consider replacing the traditional linear predictors by the more general predictors in whose case one covariate is related with the response variable in a non-parametric fashion, that we do not specified the parametric function. As an example, we could imagine a regression model in which the intercept term is believed to vary in time or geographical location. The backfitting algorithm is used for estimating the parameters of the proposed model. We perform a simulation study for assessing the behavior of the penalized maximum likelihood estimators. We use the quantile residuals for checking the assumption of the model. Finally, we analyzed real data set related with pH rivers in Ireland.

关键词： Backfitting algorithm cubic splines generalized linear models partial linear model symmetrical distributions

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Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators

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STATISTICAL METHODS AND APPLICATIONS 2021年第3期30卷 973-1005页

作者： Basu, Ayanendranath Ghosh, Abhik Mandal, Abhijit Martin, Nirian Pardo, Leandro Indian Stat Inst Interdisciplinary Stat Res Unit ISRU 203 BT Rd Kolkata 700108 W Bengal India Wayne State Univ Dept Math 656 W Kirby Detroit MI 48202 USA Univ Complutense Madrid Interdisciplinary Math Inst Madrid 28003 Spain Univ Complutense Madrid Dept Financial & Actuarial Econ & Stat Madrid 28003 Spain Univ Complutense Madrid Interdisciplinary Math Inst Madrid 28040 Spain Univ Complutense Madrid Dept Stat & ORI Madrid 28040 Spain

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.

关键词： generalized linear models Minimum density power divergence estimator Wald-type tests Robustness

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Surprise sampling: Improving and extending the local case-control sampling

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ELECTRONIC JOURNAL OF STATISTICS 2021年第1期15卷 2454-2482页

作者： Shen, Xinwei Chen, Kani Yu, Wen Hong Kong Univ Sci & Technol Dept Math Hong Kong Peoples R China Fudan Univ Sch Management Dept Stat Shanghai Peoples R China

Fithian & Hastie [7] proposed a sampling scheme called local case-control (LCC) sampling that achieves stability and efficiency by utilizing a clever adjustment pertained to the logistic model. It is particularly useful for classification with large and imbalanced data. This paper proposes a more general sampling scheme based on a working principle that data points deserve higher sampling probability if they contain more information or appear "surprising" in the sense of, for example, a large error of pilot prediction or a large absolute score. Compared with the relevant existing sampling schemes, as reported in [7] and [1], the proposed one has several advantages. It adaptively gives out the optimal forms to a variety of objectives, including the LCC and [1] as special cases. Under same model specifications, the proposed estimator also performs no worse than those in the literature. The estimation procedure is valid even if the model is misspecified and/or the pilot estimator is inconsistent or dependent on full data. We present theoretical justifications of the claimed advantages and optimality of the estimation and the sampling design. Different from [1], our large sample theory are population-wise rather than data-wise. Moreover, the proposed approach can be applied to unsupervised learning studies, since it essentially only requires a specific loss function and no response-covariate structure of data is needed. Numerical studies are carried out and the evidence in support of the theory is shown.

关键词： generalized linear models Horvitz-Thompson estimator local case-control sampling model mis-specification subsampling

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A new two-parameter discrete poisson-generalized Lindley distribution with properties and applications to healthcare data sets

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COMPUTATIONAL STATISTICS 2021年第4期36卷 2841-2861页

作者： Altun, Emrah Bartin Univ Dept Math Bartin Turkey

Mixed-Poisson distributions have been used in many fields for modeling the over-dispersed count data sets. To open a new opportunity in modeling the over-dispersed count data sets, we introduce a new mixed-Poisson distribution using the generalized Lindley distribution as a mixing distribution. The moment and probability generating functions, factorial moments as well as skewness, and kurtosis measures are derived. Using the mean-parametrized version of the proposed distribution, we introduce a new count regression model which is an appropriate model for over-dispersed counts. The healthcare data sets are analyzed employing a new count regression model. We conclude that the new regression model works well in the case of over-dispersion.

关键词： Exact distribution theory generalized linear models Count data Over-dispersion

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