GLMlike

GLMlike is a term used in statistics to describe models that are structurally similar to generalized linear models (GLMs) but that relax or modify one or more of GLM’s core components. In a GLM, the response distribution is drawn from the exponential family; the linear predictor η = Xβ enters through a link function g so that g(μ) = η; and a dispersion parameter governs variability. GLMlike models preserve the basic idea of a link between predictors and the mean response but extend beyond the strict GLM framework in various ways.

Common GLMlike extensions include quasi-likelihood or quasi-GLMs that allow overdispersion not captured by the canonical GLM distribution; GLMs with flexible or varying link functions; GLMs with non-constant variance structures; additive or non-linear transformations of the linear predictor while maintaining a GLM-like interpretation; and mixed-effects variants that introduce random effects within a GLM-like formulation.

Estimation and interpretation in GLMlike models often rely on iterative or quasi-likelihood methods, maximum likelihood, or quasi-likelihood approaches. Parameter estimates are interpreted as the effects of covariates on the mean outcome via the chosen link function, similar to GLMs, but with the understanding that the underlying distributional assumptions or variance structure may differ from a strict GLM.

Applications of GLMlike models are broad, encompassing non-Gaussian data such as counts, binary outcomes, and overdispersed data. They are used in fields including epidemiology, ecology, and social sciences, where the classic GLM assumptions are too restrictive but a GLM-like framework remains a convenient and interpretable modeling approach.