Branch and Bound to Assess Stability of Regression Coefficients in Uncertain Models
This addresses the challenge of coefficient stability for researchers working with high-dimensional regression models, though it is incremental as it applies an existing algorithmic approach to a known bottleneck.
The paper tackles the problem of interpreting regression coefficients in uncertain models by efficiently searching for their maximum and minimum values over a discrete space of regularized regression models using a branch and bound algorithm, providing a tool for researchers to assess coefficient stability in high-dimensional data.
It can be difficult to interpret a coefficient of an uncertain model. A slope coefficient of a regression model may change as covariates are added or removed from the model. In the context of high-dimensional data, there are too many model extensions to check. However, as we show here, it is possible to efficiently search, with a branch and bound algorithm, for maximum and minimum values of that adjusted slope coefficient over a discrete space of regularized regression models. Here we introduce our algorithm, along with supporting mathematical results, an example application, and a link to our computer code, to help researchers summarize high-dimensional data and assess the stability of regression coefficients in uncertain models.