Full Credibility with Generalized Linear and Mixed Models

2009 ◽  
Vol 39 (1) ◽  
pp. 61-80 ◽  
Author(s):  
José Garrido ◽  
Jun Zhou
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Link Function ◽  
Analysis Method ◽  
Risk Class ◽  
Statistical Analysis Method ◽  
Car Insurance ◽  
Insurance Data

AbstractGeneralized linear models (GLMs) are gaining popularity as a statistical analysis method for insurance data. For segmented portfolios, as in car insurance, the question of credibility arises naturally; how many observations are needed in a risk class before the GLM estimators can be considered credible? In this paper we study the limited fluctuations credibility of the GLM estimators as well as in the extended case of generalized linear mixed model (GLMMs). We show how credibility depends on the sample size, the distribution of covariates and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.

Generalized linear mixed models for multi-reader multi-case studies of diagnostic tests

2015 ◽  
Vol 26 (3) ◽  
pp. 1373-1388 ◽  
Author(s):  
Wei Liu ◽  
Norberto Pantoja-Galicia ◽  
Bo Zhang ◽  
Richard M Kotz ◽  
Gene Pennello ◽  
...  
Keyword(s):  
Mixed Models ◽  
Diagnostic Tests ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Models ◽  
Characteristic Curve ◽  
Linear Mixed Models ◽  
Parametric Bootstrap ◽  
Pseudo Likelihood

Diagnostic tests are often compared in multi-reader multi-case (MRMC) studies in which a number of cases (subjects with or without the disease in question) are examined by several readers using all tests to be compared. One of the commonly used methods for analyzing MRMC data is the Obuchowski–Rockette (OR) method, which assumes that the true area under the receiver operating characteristic curve (AUC) for each combination of reader and test follows a linear mixed model with fixed effects for test and random effects for reader and the reader–test interaction. This article proposes generalized linear mixed models which generalize the OR model by incorporating a range-appropriate link function that constrains the true AUCs to the unit interval. The proposed models can be estimated by maximizing a pseudo-likelihood based on the approximate normality of AUC estimates. A Monte Carlo expectation-maximization algorithm can be used to maximize the pseudo-likelihood, and a non-parametric bootstrap procedure can be used for inference. The proposed method is evaluated in a simulation study and applied to an MRMC study of breast cancer detection.

Linear mixed model better than repeated measures analysis

2019 ◽  
Vol 30 (6) ◽  
pp. NP1-NP2 ◽  
Author(s):  
Işıl Kutluturk Karagoz ◽  
Berhan Keskin ◽  
Flora Özkalaycı ◽  
Ali Karagöz
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Time ◽  
Case Series ◽  
Model Fit ◽  
Repeated Measures Analysis ◽  
Technical Issues ◽  
Better Than

We have some criticism regarding some technical issues. Mixed models have begun to play a pivotal role in statistical analyses and offer many advantages over more conventional analyses regarding repeated variance analyses. First, they allow to avoid conducting multiple t-tests; second, they can accommodate for within-patient correlation; third, they allow to incorporate not only a random coefficient, but also a random slope, typically ‘linear’ time in longitudinal case series when there are enough data and patients’ trajectories vary a lot and improving model fit.

scholarly journals Characterizing Heterogeneity of Disease Incidence in a Spatial Hierarchy: A Case Study from a Decade of Observations of Fusarium Head Blight of Wheat

2012 ◽  
Vol 102 (9) ◽  
pp. 867-877 ◽  
Author(s):  
A. B. Kriss ◽  
P. A. Paul ◽  
L. V. Madden
Keyword(s):  
Spatial Heterogeneity ◽  
Fusarium Head Blight ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Disease Incidence ◽  
Geographical Location ◽  
Disease Status ◽  
Link Function ◽  
Head Blight ◽  
Growing Seasons

A multilevel analysis of heterogeneity of disease incidence was conducted based on observations of Fusarium head blight (caused by Fusarium graminearum) in Ohio during the 2002–11 growing seasons. Sampling consisted of counting the number of diseased and healthy wheat spikes per 0.3 m of row at 10 sites (about 30 m apart) in a total of 67 to 159 sampled fields in 12 to 32 sampled counties per year. Incidence was then determined as the proportion of diseased spikes at each site. Spatial heterogeneity of incidence among counties, fields within counties, and sites within fields and counties was characterized by fitting a generalized linear mixed model to the data, using a complementary log-log link function, with the assumption that the disease status of spikes was binomially distributed conditional on the effects of county, field, and site. Based on the estimated variance terms, there was highly significant spatial heterogeneity among counties and among fields within counties each year; magnitude of the estimated variances was similar for counties and fields. The lowest level of heterogeneity was among sites within fields, and the site variance was either 0 or not significantly greater than 0 in 3 of the 10 years. Based on the variances, the intracluster correlation of disease status of spikes within sites indicated that spikes from the same site were somewhat more likely to share the same disease status relative to spikes from other sites, fields, or counties. The estimated best linear unbiased predictor (EBLUP) for each county was determined, showing large differences across the state in disease incidence (as represented by the link function of the estimated probability that a spike was diseased) but no consistency between years for the different counties. The effects of geographical location, corn and wheat acreage per county, and environmental conditions on the EBLUP for each county were not significant in the majority of years.

Does Sample Attrition Affect the Assessment of Frailty Trajectories Among Older Adults? A Joint Model Approach

Gerontology ◽  
2018 ◽  
Vol 64 (5) ◽  
pp. 430-439 ◽  
Author(s):  
Erwin Stolz ◽  
Hannes Mayerl ◽  
Éva Rásky ◽  
Wolfgang Freidl
Keyword(s):  
Older Adults ◽  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Mixed Models ◽  
Joint Model ◽  
Joint Models ◽  
Sample Attrition ◽  
Standard Linear ◽  
The Impact

Background: Frailty constitutes an important risk factor for adverse outcomes among older adults. In longitudinal studies on frailty, selective sample attrition may threaten the validity of results. Objective: To assess the impact of sample attrition on frailty index trajectories and gaps related to socio-economic status (education) therein among older adults in Europe. Methods: A total of 64,143 observations from 21,044 respondents (50+) from the Survey of Health, Ageing and Retirement in Europe across 12 years of follow-up (2004–2015) and subject to substantial sample attrition (59%) were analysed. We compared results of a standard linear mixed model assuming missing at random (MAR) sample attrition with a joint model assuming missing not at random sample attrition. Results: Estimated frailty trajectories of both the mixed and joint models were identical up to an age of 80 years, above which modest underestimation occurred when a standard linear mixed model was used rather than a joint model. The latter effect was larger for men than women. Substantial education-based inequality in frailty continued throughout old age in both the mixed and joint models. Conclusion: Linear mixed models assuming MAR sample attrition provided good estimates of frailty trajectories up until high age. Thus, the validity of existing studies estimating frailty trajectories based on standard linear mixed models seems not threatened by substantial sample attrition.

scholarly journals Sigmoidal mixed models for longitudinal data

2016 ◽  
Vol 27 (3) ◽  
pp. 863-875 ◽  
Author(s):  
Ana W Capuano ◽  
Robert S Wilson ◽  
Sue E Leurgans ◽  
Jeffrey D Dawson ◽  
David A Bennett ◽  
...  
Keyword(s):  
Cognitive Decline ◽  
Mixed Models ◽  
Mixed Model ◽  
Linear Models ◽  
Polynomial Regression ◽  
Piecewise Linear ◽  
Model Misspecification ◽  
Cognitive Testing ◽  
Family Of Curves ◽  
Rate Of Decline

Linear mixed models are widely used to analyze longitudinal cognitive data. Often, however, the trajectory of cognitive function is nonlinear. For example, some participants may experience cognitive decline that accelerates as death approaches. Polynomial regression and piecewise linear models are common approaches used to characterize nonlinear trajectories, although both have assumptions that may not correspond with the actual trajectories. An alternative is to use a flexible sigmoidal mixed model based on the logistic family of curves. We describe a general class of such a model, which has up to five parameters, representing (1) final level, (2) rate of decline, (3) midpoint of decline, (4) initial level before decline, and (5) asymmetry. Focusing on a four-parameter symmetric sub-class of the model, with random effects on two of the parameters, we demonstrate that a likelihood approach to fitting this model produces accurate estimates of mean levels across time, even in the case of model misspecification. We also illustrate the method on deceased participants who had completed at least 5 years of annual cognitive testing and annual assessment of body mass. We show that departures from a stable body can modify the trajectory curves and anticipate cognitive decline.

Spain retains its title and sets a new record – generalized linear mixed models on European football championships

2013 ◽  
Vol 9 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Andreas Groll ◽  
Jasmin Abedieh
Keyword(s):  
Variable Selection ◽  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Poisson Model ◽  
Penalty Term ◽  
Sparse Model ◽  
Cluster Data ◽  
European Football

AbstractNowadays many approaches that analyze and predict the results of football matches are based on bookmakers’ ratings. It is commonly accepted that the models used by the bookmakers contain a lot of expertise as the bookmakers’ profits and losses depend on the performance of their models. One objective of this article is to analyze the role of bookmakers’ odds together with many additional, potentially influental covariates with respect to a national team’s success at European football championships and especially to detect covariates, which are able to explain parts of the information covered by the odds. Therefore a pairwise Poisson model for the number of goals scored by national teams competing in European football championship matches is used. Moreover, the generalized linear mixed model (GLMM) approach, which is a widely used tool for modeling cluster data, allows to incorporate team-specific random effects. Two different approaches to the fitting of GLMMs incorporating variable selection are used, subset selection as well as a Lasso-type technique, including an L1-penalty term that enforces variable selection and shrinkage simultaneously. Based on the two preceeding European football championships a sparse model is obtained that is used to predict all matches of the current tournament resulting in a possible course of the European football championship (EURO) 2012.

Measuring growth patterns in the field: effects of sampling regime and methods on standardized estimates

2011 ◽  
Vol 89 (6) ◽  
pp. 529-537 ◽  
Author(s):  
J.G.A. Martin ◽  
F. Pelletier
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Mixed Model ◽  
Linear Models ◽  
Simulated Data ◽  
Growth Patterns ◽  
Repeated Measurements ◽  
Least Squares Regression ◽  
Sampling Regime ◽  
Parturition Date

Although mixed effects models are widely used in ecology and evolution, their application to standardized traits that change within season or across ontogeny remains limited. Mixed models offer a robust way to standardize individual quantitative traits to a common condition such as body mass at a certain point in time (within a year or across ontogeny), or parturition date for a given climatic condition. Currently, however, most researchers use simple linear models to accomplish this task. We use both empirical and simulated data to underline the application of mixed models for standardizing trait values to a common environment for each individual. We show that mixed model standardizations provide more accurate estimates of mass parameters than linear models for all sampling regimes and especially for individuals with few repeated measures. Our simulations and analyses on empirical data both confirm that mixed models provide a better way to standardize trait values for individuals with repeated measurements compared with classical least squares regression. Linear regression should therefore be avoided to adjust or standardize individual measurements

scholarly journals Prediction of Friction Degradation in Highways with Linear Mixed Models

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 187
Author(s):  
Adriana Santos ◽  
Elisabete F. Freitas ◽  
Susana Faria ◽  
Joel R. M. Oliveira ◽  
Ana Maria A. C. Rocha
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Mixed Models ◽  
Pavement Management ◽  
Climate Conditions ◽  
Pavement Management Systems ◽  
Geometrical Features ◽  
Highway Network ◽  
Network Manager

The development of a linear mixed model to describe the degradation of friction on flexible road pavements to be included in pavement management systems is the aim of this study. It also aims at showing that, at the network level, factors such as temperature, rainfall, hypsometry, type of layer, and geometric alignment features may influence the degradation of friction throughout time. A dataset from six districts of Portugal with 7204 sections was made available by the Ascendi Concession highway network. Linear mixed models with random effects in the intercept were developed for the two-level and three-level datasets involving time, section and district. While the three-level models are region-specific, the two-level models offer the possibility to be adopted to other areas. For both levels, two approaches were made: One integrating into the model only the variables inherent to traffic and climate conditions and the other including also the factors intrinsic to the highway characteristics. The prediction accuracy of the model was improved when the variables hypsometry, geometrical features, and type of layer were considered. Therefore, accurate predictions for friction evolution throughout time are available to assist the network manager to optimize the overall level of road safety.

scholarly journals Non-linear Mixed Models in a Dose Response Modelling

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Madona Yunita Wijaya
Keyword(s):  
Linear Model ◽  
Dose Response ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Growth Curves ◽  
Limiting Factor ◽  
Dose Time ◽  
Non Linear ◽  
Diffusion Function

AbstractStudy designs in which an outcome is measured more than once from time to time result in longitudinal data. Most of the methodological works have been done in the setting of linear and generalized linear models, where some amount of linearity is retained. However, this still be considered a limiting factor and non-linear models is another option offering its flexibility. Non-linear model involves complexity of non-linear dependence on parameters than that in the generalized linear class. It has been utilized in many situations such as modeling of growth curves and dose-response modeling. The latter modeling will be the main interest in this study to construct a dose-response relationship, as a function of time to IBD (inflammatory bowel disease) dataset. The dataset comes from a clinical trial with 291 subjects measured during a 7 week period. Both linear and non-linear models are considered. A dose time response model with generalized diffusion function is utilized for the non-linear models. The fit of non-linear models are found to be more flexible than linear models hence able to capture more variability present in the data.Keywords: IBD; longitudinal; linear mixed model; non-linear mixed model. AbstrakDesain studi dimana hasil diukur berulang kali dari waktu ke waktu menghasilkan data longitudinal. Sebagian besar metodologi yang digunakan untuk menganalisis data longitudinal adalah model linear dan model linear umum (generalized linear model) dimana sejumlah linearitas tertentu dipertahankan. Asumsi linearitas ini masih dipandang memiliki keterbatasan dan model non-linear adalah pilihan metode lainnya yang menawarkan fleksibilitas. Model non-linear telah digunakan di berbagai macam situasi seperti model kurva pertumbuhan , model farmakokinetika, dan farmakodinamika, dan model respon-dosis. Model respon-dosis akan menjadi fokus dalam penelitian ini untuk membangun hubungan dosis-respon sebagai fungsi waktu dari data IBD dengan menggunakan model linear dan non-linear. Hasil penelitian menunjukan bahwa model non-linear lebih fleksibel daripada model linear sehingga mampu menangkap lebih banyak variabilitas yang ada di dalam data.Keywords: IBD; longitudinal; model linear; model non-linear.

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