Estimation of mean squared prediction error of empirically spatial predictor of small area means under a linear mixed model

2020 ◽  
Vol 208 ◽  
pp. 82-93 ◽  
Author(s):  
Mahmoud Torabi ◽  
Jiming Jiang
Keyword(s):  
Prediction Error ◽  
Small Area ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Mean Squared Prediction Error ◽  
Squared Prediction Error

scholarly journals Differential Privacy Applications to Bayesian and Linear Mixed Model Estimation

2013 ◽  
Vol 5 (1) ◽  
Author(s):  
John M. Abowd ◽  
Matthew J. Schneider ◽  
Lars Vilhuber
Keyword(s):  
Random Effects ◽  
Small Area ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Differential Privacy ◽  
Predictive Distribution ◽  
Random Errors ◽  
Time Dimension ◽  
Posterior Predictive Distribution ◽  
Computationally Intensive

We consider a particular maximum likelihood estimator (MLE) and a computationally intensive Bayesian method for differentially private estimation of the linear mixed-effects model (LMM) with normal random errors. The LMM is important because it is used in small-area estimation and detailed industry tabulations that present significant challenges for confidentiality protection of the underlying data. The differentially private MLE performs well compared to the regular MLE, and deteriorates as the protection increases for a problem in which the small-area variation is at the county level. More dimensions of random effects are needed to adequately represent the time dimension of the data, and for these cases the differentially private MLE cannot be computed. The direct Bayesian approach for the same model uses an informative, reasonably diffuse prior to compute the posterior predictive distribution for the random effects. The empirical differential privacy of this approach is estimated by direct computation of the relevant odds ratios after deleting influential observations according to various criteria.

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