scholarly journals Extension and Application of Credibility Models in Predicting Claim Frequency

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yuan-tao Xie ◽  
Zheng-xiao Li ◽  
Rahul A. Parsa
Keyword(s):  
Mixed Models ◽  
Negative Binomial ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Actuarial Science ◽  
Underlying Assumption ◽  
Binomial Distributions ◽  
Numerical Studies ◽  
Proposed Model ◽  
Claim Frequency

In nonlife actuarial science, credibility models are one of the main methods of experience ratemaking. Bühlmann-Straub credibility model can be expressed as a special case of linear mixed models (LMMs) with the underlying assumption of normality. In this paper, we extend the assumption of Bühlmann-Straub model to include Poisson and negative binomial distributions as they are more appropriate for describing the distribution of a number of claims. By using the framework of generalized linear mixed models (GLMMs), we obtain the generalized credibility premiums that contain as particular cases another credibility premium in the literature. Compared to generalized linear mixed models, our extended credibility models also have an advantage in that the credibility factor falls into the range from 0 to 1. The performance of our models in comparison with an existing model in the literature is also evaluated through numerical studies, which shows that our approach produces premium estimates close to the optima. In addition, our proposed model can also be applied to the most commonly used ratemaking approach, namely, the net, the optimal Bonus-Malus system.

scholarly journals Within- and Between-cluster Effects in Generalized Linear Mixed Models: A Discussion of Approaches and the Xthybrid command

2017 ◽  
Vol 17 (1) ◽  
pp. 89-115 ◽  
Author(s):  
Reinhard Schunck ◽  
Francisco Perales
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Negative Binomial ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Consistent Estimation ◽  
Random Effects Models ◽  
Fixed Effects Models ◽  
Correlated Random Effects

One typically analyzes clustered data using random- or fixed-effects models. Fixed-effects models allow consistent estimation of the effects of level-one variables, even if there is unobserved heterogeneity at level two. However, these models cannot estimate the effects of level-two variables. Hybrid and correlated random-effects models are flexible modeling specifications that separate within-and between-cluster effects and allow for both consistent estimation of level-one effects and inclusion of level-two variables. In this article, we elaborate on the separation of within- and between-cluster effects in generalized linear mixed models. These models present a unifying framework for an entire class of models whose response variables follow a distribution from the exponential family (for example, linear, logit, probit, ordered probit and logit, Poisson, and negative binomial models). We introduce the user-written command xthybrid, a shell for the meglm command. xthybrid can fit a variety of hybrid and correlated random-effects models.

scholarly journals COMPARATIVE STUDY OF CATTLE TICK RESISTANCE USING GENERALIZED LINEAR MIXED MODELS

2019 ◽  
Vol 37 (1) ◽  
pp. 41
Author(s):  
Amanda Marchi MAIORANO ◽  
Thiago Santos MOTA ◽  
Ana Carolina VERDUGO ◽  
Ricardo Antonio da Silva FARIA ◽  
Beatriz Pressi Molina da SILVA ◽  
...  
Keyword(s):  
Negative Binomial Distribution ◽  
Count Data ◽  
Binomial Distribution ◽  
Mixed Models ◽  
Negative Binomial ◽  
Bos Taurus ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Tick Count ◽  
Tick Resistance

Comparison of tick resistance in Bos taurus indicus (Nelore) and Bos taurus taurus (Simmental and Caracu) subspecies was investigated utilizing generalized linear mixed models (GLMMs) with Poisson and Negative binomial distributions. Nelore animals (NE) are known to present greater resistance than t. taurus. Difference between tick resistance in Simmental (SI) and Caracu (CA) breeds has never been reported previously. Three artificial tick infestations were conducted to evaluate tick resistance in these breeds. The statistic point of the present study was to show alternative models for the evaluation of tick count data, the GLMMs. Analysis for tick resistance by GLMM with Negative binomial distribution has never been assessed previously. The analyses were performed by the use of the PROC GLIMMIX procedure of the SAS program. The results showed that GLMM with Negative binomial distribution is appropriated to evaluate tick count data with excess of zero observations avoiding overdispersion problems. Finally, considering multiple comparisons with the Bonferroni test, different pattern of tick infestation was observed for the studied breeds, suggesting that NE is the most resistant breed followed by CA.

l2-Penalized temporal logit-mixed models for the estimation of regional obesity prevalence over time

2021 ◽  
pp. 096228022110175
Author(s):  
Jan P Burgard ◽  
Joscha Krause ◽  
Ralf Münnich ◽  
Domingo Morales
Keyword(s):  
Parameter Estimation ◽  
Medical Treatment ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Obesity Prevalence ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Public Health Reporting ◽  
Over Time

Obesity is considered to be one of the primary health risks in modern industrialized societies. Estimating the evolution of its prevalence over time is an essential element of public health reporting. This requires the application of suitable statistical methods on epidemiologic data with substantial local detail. Generalized linear-mixed models with medical treatment records as covariates mark a powerful combination for this purpose. However, the task is methodologically challenging. Disease frequencies are subject to both regional and temporal heterogeneity. Medical treatment records often show strong internal correlation due to diagnosis-related grouping. This frequently causes excessive variance in model parameter estimation due to rank-deficiency problems. Further, generalized linear-mixed models are often estimated via approximate inference methods as their likelihood functions do not have closed forms. These problems combined lead to unacceptable uncertainty in prevalence estimates over time. We propose an l2-penalized temporal logit-mixed model to solve these issues. We derive empirical best predictors and present a parametric bootstrap to estimate their mean-squared errors. A novel penalized maximum approximate likelihood algorithm for model parameter estimation is stated. With this new methodology, the regional obesity prevalence in Germany from 2009 to 2012 is estimated. We find that the national prevalence ranges between 15 and 16%, with significant regional clustering in eastern Germany.

Evaluation of Community-Intervention Trials via Generalized Linear Mixed Models

Biometrics ◽  
2004 ◽  
Vol 60 (4) ◽  
pp. 1043-1052 ◽  
Author(s):  
Yutaka Yasui ◽  
Ziding Feng ◽  
Paula Diehr ◽  
Dale McLerran ◽  
Shirley A. A. Beresford ◽  
...  
Keyword(s):  
Mixed Models ◽  
Community Intervention ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Intervention Trials
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