Variance-bias Trade-off in Generalized Linear Regression Models

Open Access
Author:
Lin, Junyi
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
None
Committee Members:
  • Dr Runze Li, Thesis Advisor
  • Runze Li, Thesis Advisor
Keywords:
  • bias and variance tradeoff
  • covariate-adjusted approach
  • generalized linear model
Abstract:
The variance-bias trade-off has been partially discussed for linear and logistic regression models, but not for generalized linear models as a whole. In this paper, we derive the bias of the treatment effect in covariate-unadjusted models, when some important covariates are omitted. This result encourages the use of the covariate-adjusted approach in general. On the other hand, we show that for a broad class of generalized linear models, estimation of the treatment effect obtained from covariate-adjusted models have larger variances compared to those obtained from covariate-unadjusted models. This result reveals the potential loss of efficiency related to the covariate-adjusted approach, particularly when sample size is not large. These theoretical results are illustrated through examples, a simulation study and a real data example.