Main effects and interactions in mixed and incomplete data frames

Understand

A mixed data frame (MDF) is a table collecting categorical, numerical and count observations.

• The use of MDF is widespread in statistics and the applications are numerous from abundance data in ecology to recommender systems.
• In many cases, an MDF exhibits simultaneously main effects, such as row, column or group effects and interactions, for which a low-rank model has often been suggested.
• Although the literature on low-rank approximations is very substantial, with few exceptions, existing methods do not allow to incorporate main effects and interactions while providing statistical guarantees.