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/Co-Advisor Runze Li, Thesis Advisor/Co-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.
