This article provides a concise and accessible overview of Generalized Quasi-Likelihood (GQL) inference, an approach that extends classical likelihood theory to cases where specifying a complete likelihood is difficult or impractical. GQL constructs a quasi-likelihood function that retains essential properties of the likelihood without requiring full probabilistic specification.
The quasi-likelihood framework is especially useful in complex or semi-parametric models, including generalized linear models (GLMs), where assumptions like independence or precise distributional form may not hold. By utilizing a "working model" to approximate the true data-generating process, GQL offers a flexible and computationally viable tool for inference.
The article outlines practical strategies for implementing GQL inference using mainstream statistical software. In R, packages like stats,
glm, and bbmle are adaptable to GQL-style methods. Python's Statsmodels and Scikit-learn provide similar flexibility.
Commercial tools like SAS (PROC GENMOD) and Stata (glm) also support GQL-type modeling through customized link and variance functions.
The paper reviews recent contributions in the field by Fan et al. (2012), Kim (2014), Rao et al. (2012), Atchade & Bhattacharyya (2019), and others. These studies underscore GQL’s relevance for panel data, dynamic mixed models, and quasi-Bayesian frameworks.
In sum, GQL provides a robust and adaptable framework for situations where classical likelihood inference falters. It bridges the gap between rigid parametric assumptions and practical, data-driven model fitting, making it a valuable tool for modern statisticians working with complex or partially specified models.
For technical details, implementation examples, and recent research, refer to the full article in the International Encyclopedia of Statistical Science.