scholarly journals A CREDIBILITY APPROACH FOR COMBINING LIKELIHOODS OF GENERALIZED LINEAR MODELS

2016 ◽  
Vol 46 (3) ◽  
pp. 531-569 ◽  
Author(s):  
Marcus C. Christiansen ◽  
Edo Schinzinger
Keyword(s):  
Generalized Linear Models ◽  
Empirical Bayes ◽  
Linear Models ◽  
Claims Data ◽  
Model Fitting ◽  
Bayes Estimation ◽  
Credibility Estimator ◽  
Borrowing Strength ◽  
Insurance Claims Data ◽  
Mortality Modelling

AbstractGeneralized linear models are a popular tool for the modelling of insurance claims data. Problems arise with the model fitting if little statistical information is available. In case that related statistics are available, statistical inference can be improved with the help of the borrowing-strength principle. We present a credibility approach that combines the maximum likelihood estimators of individual canonical generalized linear models in a meta-analytic way to an improved credibility estimator. We follow the concept of linear empirical Bayes estimation, which reduces the necessary parametric assumptions to a minimum. The concept is illustrated by a simulation study and an application example from mortality modelling.

scholarly journals eNetXplorer: an R package for the quantitative exploration of elastic net families for generalized linear models

2018 ◽  
Author(s):  
Julián Candia ◽  
John S. Tsang
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Statistical Significance ◽  
Model Fitting ◽  
Predictive Performance ◽  
R Package ◽  
Research Area ◽  
Elastic Net ◽  
Feature Identification ◽  
Practical Applications

AbstractBackgroundRegularized generalized linear models (GLMs) are popular regression methods in bioinformatics, particularly useful in scenarios with fewer observations than parameters/features or when many of the features are correlated. In both ridge and lasso regularization, feature shrinkage is controlled by a penalty parameter λ. The elastic net introduces a mixing parameter α to tune the shrinkage continuously from ridge to lasso. Selecting α objectively and determining which features contributed significantly to prediction after model fitting remain a practical challenge given the paucity of available software to evaluate performance and statistical significance.ResultseNetXplorer builds on top of glmnet to address the above issues for linear (Gaussian), binomial (logistic), and multinomial GLMs. It provides new functionalities to empower practical applications by using a cross validation framework that assesses the predictive performance and statistical significance of a family of elastic net models (as α is varied) and of the corresponding features that contribute to prediction. The user can select which quality metrics to use to quantify the concordance between predicted and observed values, with defaults provided for each GLM. Statistical significance for each model (as defined by α) is determined based on comparison to a set of null models generated by random permutations of the response; the same permutation-based approach is used to evaluate the significance of individual features. In the analysis of large and complex biological datasets, such as transcriptomic and proteomic data, eNetXplorer provides summary statistics, output tables, and visualizations to help assess which subset(s) of features have predictive value for a set of response measurements, and to what extent those subset(s) of features can be expanded or reduced via regularization.ConclusionsThis package presents a framework and software for exploratory data analysis and visualization. By making regularized GLMs more accessible and interpretable, eNetXplorer guides the process to generate hypotheses based on features significantly associated with biological phenotypes of interest, e.g. to identify biomarkers for therapeutic responsiveness. eNetXplorer is also generally applicable to any research area that may benefit from predictive modeling and feature identification using regularized GLMs.Availability and implementationThe package is available under GPL-3 license at the CRAN repository, https://CRAN.R-project.org/package=eNetXplorer

scholarly journals Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling

2002 ◽  
Vol 32 (1) ◽  
pp. 143-157 ◽  
Author(s):  
Gordon K. Smyth ◽  
Bent Jørgensen
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Likelihood Function ◽  
Poisson Model ◽  
Insurance Claims ◽  
Poisson Arrival ◽  
Insurance Claims Data ◽  
The Cost ◽  
Insurance Data

AbstractWe reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

scholarly journals Bayes and Empirical Bayes Estimation for the Chain Ladder Model

1990 ◽  
Vol 20 (2) ◽  
pp. 217-243 ◽  
Author(s):  
R.J. Verrall
Keyword(s):  
Empirical Bayes ◽  
Linear Models ◽  
Bayes Estimation ◽  
Estimation Methods ◽  
Empirical Bayes Estimation ◽  
Collateral Information ◽  
Classical Formulation ◽  
The Subject ◽  
Modelling Assumptions ◽  
Chain Ladder

AbstractThe subject of predicting outstanding claims on a porfolio of general insurance policies is approached via the theory of hierarchical Bayesian linear models. This is particularly appropriate since the chain ladder technique can be expressed in the form of a linear model. The statistical methods which are applied allow the practitioner to use different modelling assumptions from those implied by a classical formulation, and to arrive at forecasts which have a greater degree of inherent stability. The results can also be used for other linear models. By using a statistical structure, a sound approach to the chain ladder technique can be derived. The Bayesian results allow the input of collateral information in a formal manner. Empirical Bayes results are derived which can be interpreted as credibility estimates. The statistical assumptions which are made in the modelling procedure are clearly set out and can be tested by the practitioner. The results based on the statistical theory form one part of the reserving procedure, and should be followed by expert interpretation and analysis. An illustration of the use of Bayesian and empirical Bayes estimation methods is given.

The Use of Migraine Preventive Medications Among Patients with and without Migraine Headaches

Cephalalgia ◽  
2009 ◽  
Vol 30 (1) ◽  
pp. 97-104 ◽  
Author(s):  
JE Lafata ◽  
O Tunceli ◽  
M Cerghet ◽  
KP Sharma ◽  
RB Lipton
Keyword(s):  
Linear Models ◽  
Claims Data ◽  
Adherence Rate ◽  
Retrospective Case ◽  
Migraine Headaches ◽  
Medical Care Costs ◽  
Pharmacy Claims ◽  
Insurance Claims Data ◽  
Health Insurance Claims Data ◽  
Antidepressant Use

The aim was to describe the use of and adherence to migraine preventives among insured patients meeting the International Classification of Headache Disorders, 2nd edn (ICHD-II) criteria for migraine headaches. A retrospective, case–control study was conducted using data from a telephone interview linked with health insurance claims data. Subjects were health plan enrollees aged 18–55 years who had incurred at least one encounter between June 2000 and November 2001. Interview responses were used to identify cases meeting the ICHD-II criteria for strict and probable migraine and a random sample of controls. Pharmacy claims data were used to construct measures of use and adherence. Differences in outcomes by adherence status were evaluated using generalized linear models. We identified 2517 cases and 941 controls. Among cases, the prevalence of antidepressant use was 4%, anticonvulsant use was 1.9%, antihypertensive use was 8.9%. Combined use was 13.4% among cases and did not differ significantly from that observed among controls (12.4%). Mean adherence rate between the first and last dispensing during the year was high (88%) and did not differ by migraine status. When the entire 12-month period is considered, adherence was substantially lower (56%). Patients who were adherent between dispensings reported significantly less migraine-related disability and incurred higher prescription drug costs, but did not differ in their total medical care costs. Patients with migraine are unlikely to be users of preventive medications. Among users, few are taking preventive medications continuously. Patients with migraine—especially those without a medical diagnosis for migraine or headaches—are not receiving the benefits available from existing pharmacotherapy options.

scholarly journals Credibility Theory and Generalized Linear Models

1997 ◽  
Vol 27 (1) ◽  
pp. 71-82 ◽  
Author(s):  
J.A. Nelder ◽  
R.J. Verrall
Keyword(s):  
Random Effects ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Model Fitting ◽  
Credibility Theory ◽  
Hierarchical Generalized Linear Models ◽  
Testing Procedures ◽  
Standard Statistical Package ◽  
Wide Range ◽  
Extensive Range

AbstractThis paper shows how credibility theory can be encompassed within the theory of Hierarchical Generalized Linear Models. It is shown that credibility estimates are obtained by including random effects in the model. The framework of Hierarchical Generalized Linear Models allows a more extensive range of models to be used than straightforward credibility theory. The model fitting and testing procedures can be carried out using a standard statistical package. Thus, the paper contributes a further range of models which may be useful in a wide range of actuarial applications, including premium rating and claims reserving.

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