glmFit

glmFit, commonly written glmfit, is a function in MATLAB's Statistics and Machine Learning Toolbox that fits generalized linear models (GLMs) to data. It estimates model coefficients using the iteratively reweighted least squares (IRLS) algorithm and supports responses that follow distributions in the exponential family, such as normal, binomial, Poisson, and gamma. Users can specify a link function, choosing from canonical or alternative options, and may provide weights and offsets to model varying exposure or known effects.

Inputs and options: The main inputs are X, an n-by-p design matrix, and y, an n-by-1 response vector. The function accepts a distribution spec (DIST) such as 'normal', 'binomial', 'poisson', or 'gamma', and a 'link' specification. Optional inputs include 'weights' and 'offset', with additional controls accessible through an options structure created by statset. The usual call returns B, the coefficient vector including the intercept, the deviance DEV, and a stats structure with diagnostic information such as standard errors, and, if requested, t-statistics and p-values.

Outputs: B contains the estimated coefficients for the predictors and the intercept. DEV is the model deviance, reflecting the goodness of fit. STATS is a structure providing supplementary information about the fit, including covariance estimates for the coefficients, standard errors, and other diagnostic quantities useful for inference.

Applications and behavior: GLMs fitted with glmfit enable a range of common analyses, including logistic regression for binary data (binomial with a logit link), Poisson regression for count data (Poisson with a log link), and gamma regression for positive continuous data. The function supports offset terms to handle known exposure or baseline effects and can incorporate observation weights to reflect varying precision across data points.

History and context: glmfit is part of MATLAB’s Statistics and Machine Learning Toolbox and has long been used for flexible modeling of diverse data types. It complements related functions such as glmval for computing predicted responses from estimated coefficients.