Real-Time Regression Analysis of Streaming Clustered Data With Possible Abnormal Data Batches

Abstract

This article develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF) method within a paradigm of renewable estimation and incremental inference, in which parameter estimates are recursively renewed with current data and summary statistics of historical data, but with no use of any historical subject-level raw data. We compare our renewable estimation method with both offline QIF and offline generalized estimating equations (GEE) approach that process the entire cumulative subject-level data all together, and show theoretically and numerically that our renewable procedure enjoys statistical and computational efficiency. We also propose an approach to diagnose the homogeneity assumption of regression coefficients via a sequential goodness-of-fit test as a screening procedure on occurrences of abnormal data batches. We implement the proposed methodology by expanding existing Spark’s Lambda architecture for the operation of statistical inference and data quality diagnosis. We illustrate the proposed methodology by extensive simulation studies and an analysis of streaming car crash datasets from the National Automotive Sampling System-Crashworthiness Data System (NASS CDS). Supplementary materials for this article are available online.

Keywords:

• Abnormal data batch detection
• Generalized estimating equation
• Incremental statistical analysis
• Online learning
• Quadratic inference function
• Spark computing platform

Supplementary Materials

This file includes the proof of some useful lemmas in Section 1, additional details in the proof under scenario (S1) in Section 2, proof of large sample properties in scenarios (S2) and (S3) in Section 3, and the analysis of cumulative error bound in Section 4. In Section 5, we include one table and one figure from simulation studies and an additional table from real data analysis. Additionally in Section 6, we includes “Renewable GEE” with derivation of renewable estimation and incremental inference method in the generalized estimating equations. (PDF)

Acknowledgments

The authors are grateful to editor, associate editor and three anonymous reviewers for their insightful comments and constructive suggestions that help greatly improve the manuscript.

Additional information

Funding

This research was partially supported by the National Science Foundation grants DMS1811734 and DMS2113564 to Song, and the National Natural Science (Nos. 11901470, 11931014 and 11829101) and the Fundamental Research Funds for the Central Universities (Nos. JBK190904 and JBK1806002) to Zhou.