Logistic Regression Models for Aggregated Data

Abstract

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However, inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from symbolic data analysis to summarize the collection of predictor variables into histogram form, and perform inference on this summary dataset. We develop ideas based on composite likelihoods to derive an efficient one-versus-rest approximate composite likelihood model for histogram-based random variables, constructed from low-dimensional marginal histograms obtained from the full histogram. We demonstrate that this procedure can achieve comparable classification rates to the standard full data multinomial analysis and against state-of-the-art subsampling algorithms for logistic regression, but at a substantially lower computational cost. Performance is explored through simulated examples, and analyses of large supersymmetry and satellite crop classification datasets. Supplementary materials for this article are available online.