scholarly journals Efficient moment calculations for variance components in large unbalanced crossed random effects models

2017 ◽  
Vol 11 (1) ◽  
pp. 1235-1296 ◽  
Author(s):  
Katelyn Gao ◽  
Art Owen
Keyword(s):  
Random Effects ◽  
Variance Components ◽  
Random Effects Models ◽  
Crossed Random Effects

scholarly journals Scalable inference for crossed random effects models

Biometrika ◽  
2019 ◽  
Author(s):  
O Papaspiliopoulos ◽  
G O Roberts ◽  
G Zanella
Keyword(s):  
Random Effects ◽  
Gibbs Sampler ◽  
Convergence Rates ◽  
Simple Modification ◽  
Random Effects Models ◽  
Monte Carlo Algorithms ◽  
Alternative State ◽  
Crossed Random Effects ◽  
Scalable Inference ◽  
Modern Analysis

Summary We develop methodology and complexity theory for Markov chain Monte Carlo algorithms used in inference for crossed random effects models in modern analysis of variance. We consider a plain Gibbs sampler and propose a simple modification, referred to as a collapsed Gibbs sampler. Under some balancedness conditions on the data designs and assuming that precision hyperparameters are known, we demonstrate that the plain Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data, but the collapsed Gibbs sampler is scalable. In simulated and real datasets we show that the explicit convergence rates predicted by our theory closely match the computable, but nonexplicit rates in cases where the design assumptions are violated. We also show empirically that the collapsed Gibbs sampler extended to sample precision hyperparameters significantly outperforms alternative state-of-the-art algorithms.

Improved $U$-tests for variance components in one-way random effects models

2020 ◽  
Vol 34 (3) ◽  
pp. 464-477
Author(s):  
Juvêncio Santos Nobre ◽  
Julio M. Singer ◽  
Maria J. Batista
Keyword(s):  
Random Effects ◽  
Variance Components ◽  
Random Effects Models

scholarly journals Effects of Cluster Sizes on Variance Components in Two-Stage Sampling

2015 ◽  
Vol 31 (4) ◽  
pp. 763-782
Author(s):  
Richard Valliant ◽  
Jill A. Dever ◽  
Frauke Kreuter
Keyword(s):  
Sample Size ◽  
Random Effects ◽  
Variance Components ◽  
Sample Size Calculation ◽  
Household Surveys ◽  
Sample Design ◽  
Two Stage ◽  
Random Effects Models ◽  
Standard Software ◽  
The U.S

Abstract Determining sample sizes in multistage samples requires variance components for each stage of selection. The relative sizes of the variance components in a cluster sample are dramatically affected by how much the clusters vary in size, by the type of sample design, and by the form of estimator used. Measures of the homogeneity of survey variables within clusters are related to the variance components and affect the numbers of sample units that should be selected at each stage to achieve the desired precision levels. Measures of homogeneity can be estimated using standard software for random-effects models but the model-based intracluster correlations may need to be transformed to be appropriate for use with the sample design. We illustrate these points and implications for sample size calculation for two-stage sample designs using a realistic population derived from household surveys and the decennial census in the U.S.

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