Statistical Inference for Data Integration

In the age of big data, data integration is a critical step especially in the understanding of how diverse data types work together and work separately. Among the data integration methods, the Angle-Based Joint and Individual Variation Explained (AJIVE) is particularly attractive because it not only studies joint behavior but also individual behavior. Typically scores indicate relationships between data objects. The drivers of those relationships are determined by the loadings. A fundamental question is which loadings are statistically significant. A useful approach for assessing this is the jackstraw method. In this paper, we develop jackstraw for the loadings of the AJIVE data analysis. This provides statistical inference about the drivers in both joint and individual feature spaces.