Low-rank model with covariates for count data with missing values

A complete methodology called LORI (Low-Rank Interaction), including a Poisson model, an algorithm, and an automatic selection of the regularization parameter, is proposed for the analysis of frequency tables with covariates, including an upper bound on the estimation error. A simulation study with synthetic data suggests that LORI improves empirically on state-of-the-art methods in terms of estimation and imputation. Illustrations show how the method can be interpreted through visual displays with the analysis of a well-known plant abundance data set, and the LORI outputs are seen to be consistent with known results. The relevance of the methodology is also demonstrated through the analysis of a waterbirds abundance contingency table from the French national agency for wildlife and hunting management. The method is available in the R package lori on the Comprehensive Archive Network (CRAN).