An Application of Differentially Private Linear Mixed Modeling

We consider a differentially private MLE for the linear mixed-effects model with normal random errors. This model is important because it is frequently used in small area estimation and detailed industry tabulations that present significant challenges for confidentiality protection of the underlying data. The differentially private estimator performs well compared to the regular MLE, and deteriorates as the protection increases, for a problem in which 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.