ﻻ يوجد ملخص باللغة العربية
The cost of both generalized least squares (GLS) and Gibbs sampling in a crossed random effects model can easily grow faster than $N^{3/2}$ for $N$ observations. Ghosh et al. (2020) develop a backfitting algorithm that reduces the cost to $O(N)$. Here we extend that method to a generalized linear mixed model for logistic regression. We use backfitting within an iteratively reweighted penalized least square algorithm. The specific approach is a version of penalized quasi-likelihood due to Schall (1991). A straightforward version of Schalls algorithm would also cost more than $N^{3/2}$ because it requires the trace of the inverse of a large matrix. We approximate that quantity at cost $O(N)$ and prove that this substitution makes an asymptotically negligible difference. Our backfitting algorithm also collapses the fixed effect with one random effect at a time in a way that is analogous to the collapsed Gibbs sampler of Papaspiliopoulos et al. (2020). We use a symmetric operator that facilitates efficient covariance computation. We illustrate our method on a real dataset from Stitch Fix. By properly accounting for crossed random effects we show that a naive logistic regression could underestimate sampling variances by several hundred fold.
Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as $N^{3/2}$ (or worse) for $N$ observations. Papaspiliopoulos et al. (2020) present a
Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and u
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional multi-respon
For random field theory based multiple comparison corrections In brain imaging, it is often necessary to compute the distribution of the supremum of a random field. Unfortunately, computing the distribution of the supremum of the random field is not
In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the new estim