ANOVA models with random effects: an approach via symmetry

1986 ◽  
Vol 23 (A) ◽  
pp. 355-368 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Spectral Decomposition ◽  
Linear Models ◽  
Random Variables ◽  
Components Of Variance

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

ANOVA models with random effects: an approach via symmetry

1986 ◽  
Vol 23 (A) ◽  
pp. 355-368 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Spectral Decomposition ◽  
Linear Models ◽  
Random Variables ◽  
Components Of Variance

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

2013 ◽  
Vol 55 (3) ◽  
pp. 643-652
Author(s):  
Gauss M. Cordeiro ◽  
Denise A. Botter ◽  
Alexsandro B. Cavalcanti ◽  
Lúcia P. Barroso
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Covariance Matrix ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Likelihood Estimator

Influence analysis on linear models with random effects

1999 ◽  
Vol 14 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Zhong Xuping ◽  
Wei Bocheng
Keyword(s):  
Random Effects ◽  
Linear Models ◽  
Influence Analysis

scholarly journals Identification of Health Expenditures Determinants: A Model to Manage the Economic Burden of Cardiovascular Disease

2021 ◽  
Vol 18 (9) ◽  
pp. 4652
Author(s):  
Fiorella Pia Salvatore ◽  
Alessia Spada ◽  
Francesca Fortunato ◽  
Demetris Vrontis ◽  
Mariantonietta Fiore
Keyword(s):  
Cardiovascular Disease ◽  
Hospital Discharge ◽  
Random Effects ◽  
Economic Burden ◽  
Linear Models ◽  
Health Management ◽  
Model Performance ◽  
Real Data ◽  
Large Set ◽  
Regional Health

The purpose of this paper is to investigate the determinants influencing the costs of cardiovascular disease in the regional health service in Italy’s Apulia region from 2014 to 2016. Data for patients with acute myocardial infarction (AMI), heart failure (HF), and atrial fibrillation (AF) were collected from the hospital discharge registry. Generalized linear models (GLM), and generalized linear mixed models (GLMM) were used to identify the role of random effects in improving the model performance. The study was based on socio-demographic variables and disease-specific variables (diagnosis-related group, hospitalization type, hospital stay, surgery, and economic burden of the hospital discharge form). Firstly, both models indicated an increase in health costs in 2016, and lower spending values for women (p < 0.001) were shown. GLMM indicates a significant increase in health expenditure with increasing age (p < 0.001). Day-hospital has the lowest cost, surgery increases the cost, and AMI is the most expensive pathology, contrary to AF (p < 0.001). Secondly, AIC and BIC assume the lowest values for the GLMM model, indicating the random effects’ relevance in improving the model performance. This study is the first that considers real data to estimate the economic burden of CVD from the regional health service’s perspective. It appears significant for its ability to provide a large set of estimates of the economic burden of CVD, providing information to managers for health management and planning.

scholarly journals Estimation of the covariance matrix of random effects in longitudinal studies

2007 ◽  
Vol 35 (6) ◽  
pp. 2795-2814 ◽  
Author(s):  
Yan Sun ◽  
Wenyang Zhang ◽  
Howell Tong
Keyword(s):  
Longitudinal Studies ◽  
Covariance Matrix ◽  
Random Effects

scholarly journals Generalized linear models with random effects for the description of data with excess zeros

2011 ◽  
Vol 54 (6) ◽  
pp. 661-675
Author(s):  
N. Mielenz ◽  
K. Thamm ◽  
M. Bulang ◽  
J. Spilke
Keyword(s):  
Random Effects ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Linear Models ◽  
Negative Binomial ◽  
Detailed Comparison ◽  
Response Scale ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Explanatory Factors

Abstract. In this paper count data with excess zeros and repeated observations per subject are evaluated. If the number of values observed for the zero event in the trial substantially exceeds the expected number (derived from the Poisson or from the negative binomial distribution), then there is an excess of zeros. Hurdle and zero-inflated models with random effects are available in order to evaluate this type of data. In this paper both model approaches are presented and are used for the evaluation of the number of visits to the feeder per cow per hour. Finally, for the analysis of the target trait a hurdle model with random effects based on a negative binomial distribution was used. This analysis was derived from a detailed comparison of models and was needed because of a simpler computer implementation. For improved interpretation of the results, the levels of the explanatory factors (for example, the classes of lactation) were not averaged in the link scale, but rather in the response scale. The deciding explanatory variables for the pattern of visiting activities in the 24-hour cycle are the milking and cleaning times at hours 4, 7, 12 and 20. The highly significant differences in the visiting frequencies of cows of the first lactation and those of higher lactations were explained by competition for access to the feeder and thus to the feed.

scholarly journals Best linear unbiased estimation for varying probability with and without replacement sampling

2019 ◽  
Vol 7 (1) ◽  
pp. 78-91
Author(s):  
Stephen Haslett
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Linear Models ◽  
Unbiased Estimation ◽  
Error Covariance Matrix ◽  
Best Linear Unbiased Estimation ◽  
Error Covariance ◽  
Inclusion Probabilities ◽  
Best Linear Unbiased ◽  
Linear Unbiased Estimation

Abstract When sample survey data with complex design (stratification, clustering, unequal selection or inclusion probabilities, and weighting) are used for linear models, estimation of model parameters and their covariance matrices becomes complicated. Standard fitting techniques for sample surveys either model conditional on survey design variables, or use only design weights based on inclusion probabilities essentially assuming zero error covariance between all pairs of population elements. Design properties that link two units are not used. However, if population error structure is correlated, an unbiased estimate of the linear model error covariance matrix for the sample is needed for efficient parameter estimation. By making simultaneous use of sampling structure and design-unbiased estimates of the population error covariance matrix, the paper develops best linear unbiased estimation (BLUE) type extensions to standard design-based and joint design and model based estimation methods for linear models. The analysis covers both with and without replacement sample designs. It recognises that estimation for with replacement designs requires generalized inverses when any unit is selected more than once. This and the use of Hadamard products to link sampling and population error covariance matrix properties are central topics of the paper. Model-based linear model parameter estimation is also discussed.

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