An alternative REML estimation of covariance matrices in linear mixed models

2013 ◽  
Vol 83 (4) ◽  
pp. 1071-1077 ◽  
Author(s):  
Erning Li ◽  
Mohsen Pourahmadi
Keyword(s):  
Mixed Models ◽  
Linear Mixed Models ◽  
Covariance Matrices ◽  
Reml Estimation

scholarly journals lme4qtl: linear mixed models with flexible covariance structure for genetic studies of related individuals

2017 ◽  
Author(s):  
Andrey Ziyatdinov ◽  
Miquel Vázquez-Santiago ◽  
Helena Brunel ◽  
Angel Martinez-Perez ◽  
Hugues Aschard ◽  
...  
Keyword(s):  
Qtl Mapping ◽  
Random Effects ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
R Package ◽  
Covariance Matrices ◽  
Linkage Studies ◽  
Genetic Studies ◽  
Related Individuals ◽  
Mapping Models

AbstractBackgroundQuantitative trait locus (QTL) mapping in genetic data often involves analysis of correlated observations, which need to be accounted for to avoid false association signals. This is commonly performed by modeling such correlations as random effects in linear mixed models (LMMs). The R package lme4 is a well-established tool that implements major LMM features using sparse matrix methods; however, it is not fully adapted for QTL mapping association and linkage studies. In particular, two LMM features are lacking in the base version of lme4: the definition of random effects by custom covariance matrices; and parameter constraints, which are essential in advanced QTL models. Apart from applications in linkage studies of related individuals, such functionalities are of high interest for association studies in situations where multiple covariance matrices need to be modeled, a scenario not covered by many genome-wide association study (GWAS) software.ResultsTo address the aforementioned limitations, we developed a new R package lme4qtl as an extension of lme4. First, lme4qtl contributes new models for genetic studies within a single tool integrated with lme4 and its companion packages. Second, lme4qtl offers a flexible framework for scenarios with multiple levels of relatedness and becomes efficient when covariance matrices are sparse. We showed the value of our package using real family-based data in the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project.ConclusionsOur software lme4qtl enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances. lme4qtl is available at https://github.com/variani/lme4qtl.

scholarly journals Heat, Hills and the High Season: A Model-Based Comparative Analysis of Spatio-Temporal Factors Affecting Shared Bicycle Use in Three Southern European Islands

2021 ◽  
Vol 13 (6) ◽  
pp. 3274
Author(s):  
Suzanne Maas ◽  
Paraskevas Nikolaou ◽  
Maria Attard ◽  
Loukas Dimitriou
Keyword(s):  
Correlation Analysis ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Positive Association ◽  
Sustainable Mobility ◽  
Weather Factors ◽  
Gran Canaria ◽  
Bivariate Correlation ◽  
Temporal Factors

Bicycle sharing systems (BSSs) have been implemented in cities worldwide in an attempt to promote cycling. Despite exhibiting characteristics considered to be barriers to cycling, such as hot summers, hilliness and car-oriented infrastructure, Southern European island cities and tourist destinations Limassol (Cyprus), Las Palmas de Gran Canaria (Canary Islands, Spain) and the Valletta conurbation (Malta) are all experiencing the implementation of BSSs and policies to promote cycling. In this study, a year of trip data and secondary datasets are used to analyze dock-based BSS usage in the three case-study cities. How land use, socio-economic, network and temporal factors influence BSS use at station locations, both as an origin and as a destination, was examined using bivariate correlation analysis and through the development of linear mixed models for each case study. Bivariate correlations showed significant positive associations with the number of cafes and restaurants, vicinity to the beach or promenade and the percentage of foreign population at the BSS station locations in all cities. A positive relation with cycling infrastructure was evident in Limassol and Las Palmas de Gran Canaria, but not in Malta, as no cycling infrastructure is present in the island’s conurbation, where the BSS is primarily operational. Elevation had a negative association with BSS use in all three cities. In Limassol and Malta, where seasonality in weather patterns is strongest, a negative effect of rainfall and a positive effect of higher temperature were observed. Although there was a positive association between BSS use and the number of visiting tourists in Limassol and Malta, this is predominantly explained through the multi-collinearity with weather factors rather than by intensive use of the BSS by tourists. The linear mixed models showed more fine-grained results and explained differences in BSS use at stations, including differences for station use as an origin and as a destination. The insights from the correlation analysis and linear mixed models can be used to inform policies promoting cycling and BSS use and support sustainable mobility policies in the case-study cities and cities with similar characteristics.

scholarly journals Confidence, prediction, and tolerance in linear mixed models

2019 ◽  
Vol 38 (30) ◽  
pp. 5603-5622 ◽  
Author(s):  
Bernard G. Francq ◽  
Dan Lin ◽  
Walter Hoyer
Keyword(s):  
Mixed Models ◽  
Linear Mixed Models

Power for balanced linear mixed models with complex missing data processes

2021 ◽  
pp. 1-19
Author(s):  
Kevin P. Josey ◽  
Brandy M. Ringham ◽  
Anna E. Barón ◽  
Margaret Schenkman ◽  
Katherine A. Sauder ◽  
...  
Keyword(s):  
Missing Data ◽  
Mixed Models ◽  
Linear Mixed Models

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.

Estimation of variance components in normal linear mixed models with additivity

2015 ◽  
Author(s):  
Dário Ferreira ◽  
Sandra S. Ferreira ◽  
Célia Nunes ◽  
João T. Mexia
Keyword(s):  
Mixed Models ◽  
Variance Components ◽  
Linear Mixed Models ◽  
Estimation Of Variance
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