Generalized Linear Models with Missing Data
摘要
Incomplete data are a pervasive issue in infectious disease research, arising from nonresponse, administrative limitations, and the realities of observational data collection. Building on the foundations of Generalized Linear Models (GLMs), this chapter addresses the challenges posed by missing data in the context of Generalized Linear Models (GLMs). We begin by outlining the foundational distinctions between common missing data mechanisms, Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR), and discuss their implications for unbiased inference. Classical strategies such as complete-case analysis and Multiple Imputation by Chained Equations (MICE) are introduced and evaluated under varying missingness scenarios. We then present a Bayesian perspective, treating missing values as unknown parameters within the model and estimating them jointly with the regression coefficients. Using simulated and empirical examples, we demonstrate how these Bayesian methods provide coherent posterior inference and facilitate uncertainty quantification when data are incomplete. Emphasis is placed on model diagnostics, convergence evaluation, and the interpretability of resulting estimates. The approaches discussed in this chapter equip readers with practical tools for performing robust statistical modeling in the presence of incomplete information.