Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models

2008 ◽  
Vol 52 (7) ◽  
pp. 3283-3299 ◽  
Author(s):  
Fabian Scheipl ◽  
Sonja Greven ◽  
Helmut Küchenhoff
Keyword(s):  
Mixed Models ◽  
Polynomial Regression ◽  
Linear Mixed Models ◽  
Random Effect ◽  
Power Of Tests

scholarly journals Area and Resource Utilization of Group-Housed Horses in an Active Stable

Animals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 2777
Author(s):  
Frederik Hildebrandt ◽  
Kathrin Büttner ◽  
Jennifer Salau ◽  
Joachim Krieter ◽  
Irena Czycholl
Keyword(s):  
Resource Utilization ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Random Effect ◽  
Northern Germany ◽  
Heat Maps ◽  
Use Of Resources ◽  
Pasture Area

The aim of this study was to analyze the utilization of different stable areas of a total of 52 group-housed horses as well as their preferred stable parts and the use of resources. The study was situated in a “HIT Active Stable®” in Northern Germany for a period of 227 observation days. After dividing the whole farm area in a grid of 3 × 3 m, the dataset was examined with and without the pasture area. Furthermore, linear mixed models were applied. On average, horses used 53.2 ± 19 different squares per hour. The observation day (p < 0.001) and the covariate age (p < 0.001) had significant effects on the different squares visited per hour. No significant effects were found for sex (p = 0.30) and breed (p = 0.65) as only geldings and no stallions were part of the group and the distribution of the breeds was unfavorable. The random effect animal showed that the horse-individual estimates from -19.2 to 17.6 different squares visited per hour were quite large. Furthermore, it could be shown that the horses used resources such as feed stalls with a frequency of up to 0.14% more than other paddock areas without resources. Open lying halls with tarp skin were also preferred over the metal hall. The shelters were only partly popular. Use could be visualized with the help of heat maps. This study gives a good overview of the use of individual areas and resources and possible improvements.

scholarly journals Risk Adjustment for Lumbar Dysfunction: Comparison of Linear Mixed Models With and Without Inclusion of Between-Clinic Variation as a Random Effect

2015 ◽  
Vol 95 (12) ◽  
pp. 1692-1702 ◽  
Author(s):  
Sheng-Che Yen ◽  
Marie B. Corkery ◽  
Kevin K. Chui ◽  
Justin Manjourides ◽  
Ying-Chih Wang ◽  
...  
Keyword(s):  
Physical Therapy ◽  
Patient Outcomes ◽  
Risk Adjustment ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Random Effect ◽  
Fixed Effect Model ◽  
The United States ◽  
Fixed Effect ◽  
Effect Model

BackgroundValid comparison of patient outcomes of physical therapy care requires risk adjustment for patient characteristics using statistical models. Because patients are clustered within clinics, results of risk adjustment models are likely to be biased by random, unobserved between-clinic differences. Such bias could lead to inaccurate prediction and interpretation of outcomes.PurposeThe purpose of this study was to determine if including between-clinic variation as a random effect would improve the performance of a risk adjustment model for patient outcomes following physical therapy for low back dysfunction.DesignThis was a secondary analysis of data from a longitudinal cohort of 147,623 patients with lumbar dysfunction receiving physical therapy in 1,470 clinics in 48 states of the United States.MethodsThree linear mixed models predicting patients' functional status (FS) at discharge, controlling for FS at intake, age, sex, number of comorbidities, surgical history, and health care payer, were developed. Models were: (1) a fixed-effect model, (2) a random-intercept model that allowed clinics to have different intercepts, and (3) a random-slope model that allowed different intercepts and slopes for each clinic. Goodness of fit, residual error, and coefficient estimates were compared across the models.ResultsThe random-effect model fit the data better and explained an additional 11% to 12% of the between-patient differences compared with the fixed-effect model. Effects of payer, acuity, and number of comorbidities were confounded by random clinic effects.LimitationsModels may not have included some variables associated with FS at discharge. The clinics studied may not be representative of all US physical therapy clinics.ConclusionsRisk adjustment models for functional outcome of patients with lumbar dysfunction that control for between-clinic variation performed better than a model that does not.

scholarly journals Rates of Glaucoma Progression Derived from Linear Mixed Models Using Varied Random Effect Distributions

2021 ◽  
Author(s):  
Swarup Sai Swaminathan ◽  
Samuel I Berchuck ◽  
Alessandro A Jammal ◽  
J. Sunil Rao ◽  
Felipe A Medeiros
Keyword(s):  
Visual Field ◽  
Random Effects ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Random Effect ◽  
Visual Fields ◽  
Gaussian Model ◽  
Model Fit ◽  
Mean Deviation ◽  
Automated Perimetry

Purpose: To compare the ability of linear mixed models with different random effect distributions to estimate rates of visual field loss in glaucoma patients. Design: Retrospective cohort study. Methods: Eyes with ≥5 reliable standard automated perimetry (SAP) tests were identified from the Duke Glaucoma Registry. Mean deviation (MD) values from each visual field and associated timepoints were collected. These data were modeled using ordinary least square (OLS) regression as well as linear mixed models using either the Gaussian, Student t, or log-gamma (LG) distributions as the prior distribution for random effects. Model fit was compared using the Watanabe-Akaike information criterion (WAIC). Simulated eyes of varying initial disease severity and rates of progression were created to assess the accuracy of each Bayesian model in predicting the rate of change and likelihood of declaring progression. Results: A total of 52,900 visual fields from 6,558 eyes of 3,981 subjects were included. Mean follow-up period was 8.7±4.0 years, with an average of 8.1±3.7 visual fields per eye. The LG model produced the lowest WAIC, demonstrating optimal model fit. Compared to the Gaussian model, the LG model classified almost twice as many eyes as fast progressors. In simulations, the LG model declared progression earlier than OLS (P<0.001) and had the greatest accuracy in predicted slopes (P<0.001). In contrast, the Gaussian model significantly underestimated rates of progression among fast and catastrophic progressors. Conclusions: Linear mixed models using the LG distribution to model random effects outperformed conventional approaches for estimating rates of SAP MD loss in a population with glaucoma.

On the behaviour of marginal and conditional AIC in linear mixed models

Biometrika ◽  
2010 ◽  
Vol 97 (4) ◽  
pp. 773-789 ◽  
Author(s):  
Sonja Greven ◽  
Thomas Kneib
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Random Effect ◽  
Computational Cost ◽  
Information Criterion ◽  
R Package ◽  
Estimation Uncertainty ◽  
Asymptotically Unbiased Estimator ◽  
Selection Of

Abstract In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion, aic, have been used, based either on the marginal or on the conditional distribution. We show that the marginal aic is not an asymptotically unbiased estimator of the Akaike information, and favours smaller models without random effects. For the conditional aic, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that can lead to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional aic, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package (R Development Core Team, 2010) is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

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 A practical solution to pseudoreplication bias in single-cell studies

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kip D. Zimmerman ◽  
Mark A. Espeland ◽  
Carl D. Langefeld
Keyword(s):  
Single Cell ◽  
Mixed Models ◽  
Random Effect ◽  
Cell Types ◽  
Error Rates ◽  
Specific Cell ◽  
Experimental Conditions ◽  
Type 1 Error ◽  
Sample Correlation ◽  
Inflated Type

AbstractCells from the same individual share common genetic and environmental backgrounds and are not statistically independent; therefore, they are subsamples or pseudoreplicates. Thus, single-cell data have a hierarchical structure that many current single-cell methods do not address, leading to biased inference, highly inflated type 1 error rates, and reduced robustness and reproducibility. This includes methods that use a batch effect correction for individual as a means of accounting for within-sample correlation. Here, we document this dependence across a range of cell types and show that pseudo-bulk aggregation methods are conservative and underpowered relative to mixed models. To compute differential expression within a specific cell type across treatment groups, we propose applying generalized linear mixed models with a random effect for individual, to properly account for both zero inflation and the correlation structure among measures from cells within an individual. Finally, we provide power estimates across a range of experimental conditions to assist researchers in designing appropriately powered studies.

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.

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