GLMbased

GLMbased refers to analyses or methods that are based on generalized linear models (GLMs). GLMs extend linear regression to handle response variables that may not be normally distributed and relate the mean of the distribution to predictors through a link function. In a GLMbased approach, the outcome Y is assumed to follow an exponential family distribution, and the expected value μ is connected to a linear predictor η = Xβ via g(μ) = η, where g is a specified link function and X is the design matrix.

Parameters β are estimated by maximum likelihood, typically using iterative methods such as iteratively reweighted least squares or other optimization algorithms. GLMbased methods yield coefficients that describe the effect of predictors on the transformed mean; interpretation depends on the chosen link and distribution.

Common GLMbased models include logistic regression for binary outcomes, Poisson or negative binomial regression for count data, and gamma regression for positive continuous data. Extensions encompass quasi-likelihood approaches to handle overdispersion and robust standard errors, as well as mixed-effects GLMs for correlated data.

Applications span biostatistics, epidemiology, economics, social sciences, and engineering. In neuroscience and imaging, GLMbased analyses are used to model activation data; in ecology, GLMs model species counts; in marketing, they support response modeling. Software support is widespread, with implementations in R (glm), Python (statsmodels), and other statistics packages.

Limitations include potential model misspecification, independence assumptions, and sensitivity to outliers. Model diagnostics, goodness-of-fit checks, and consideration of alternative modeling frameworks (such as GLMs with additive or mixed-effects components) help address these concerns.