Yee (2010) The VGAM Package for Categorical Data Analysis

Summary

A Journal of Statistical Software paper showing that the many classical categorical-regression models — multinomial logit, proportional-odds/cumulative, adjacent-categories, continuation-ratio, stopping-ratio — are all special cases of one vector generalized linear / additive model (VGLM/VGAM) framework, and are fitted uniformly in the VGAM R package by Fisher scoring / iteratively reweighted least squares. Beyond unifying the standard models it supports natural extensions: reduced-rank VGLMs for dimension reduction, additive (smoothing) predictors, and covariates whose values are specific to each linear predictor — the structure consumer-choice / discrete-choice models need.

Key Claims

• One framework for polytomous responses. A VGLM models $M$ linear predictors $\eta_j = \boldsymbol\beta_j'\mathbf x$ simultaneously; the categorical models differ only in which functions of the multinomial probabilities the $\eta_j$ represent. VGAM's family functions enumerate them: multinomial() (baseline-category logit), cumulative() ($\Pr(Y\le j)$; proportional-odds when the slopes are shared), acat() (adjacent-categories, $\Pr(Y{=}j{+}1)/\Pr(Y{=}j)$), cratio()/sratio() (continuation-ratio / stopping-ratio).
• Shared estimation engine. All are fitted by Fisher scoring = iteratively reweighted least squares on the stacked linear predictors, so one algorithm and one inference apparatus (standard errors, deviance) serve the whole family — highlighting the models' common multinomial foundation rather than treating each with a separate function.
• Proportional-odds and its relaxation. Parallelism (equal slopes across the $\eta_j$) gives the classic proportional-odds / parallel cumulative model; relaxing the constraint on chosen covariates is a built-in option (parallel = FALSE), a partial-proportional-odds model.
• Extensions. Reduced-rank VGLMs (RR-VGLM) factor the coefficient matrix for dimension reduction (the stereotype model, row-column association models for contingency tables); VGAMs replace linear predictors with smooth additive functions; $x_{ij}$ covariates that differ across categories/alternatives accommodate discrete-choice / conditional-logit specifications.
• Software goal. Reflect the commonality of categorical models in the software so practitioners can move between them (and understand their connections) instead of using disparate, model-specific functions.

Concepts Introduced or Extended

• Ordinal Regression
• Discrete Choice Models

Entities Mentioned

• Thomas W. Yee

Quotes

"Classical categorical regression models such as the multinomial logit and proportional odds models are shown to be readily handled by the vector generalized linear and additive model (VGLM/VGAM) framework."

"Software has been slow to reflect their commonality and this makes analyses unnecessarily difficult for the practitioner ... using different functions/procedures to fit different models which does not aid the understanding of their connections."

My Take

The value here is organizational rather than a new estimator: Yee's point is that cumulative, adjacent-categories, continuation-ratio, and baseline-logit models are not a zoo of separate techniques but different link functions on the same multinomial, and once you see them as a vector GLM (several linear predictors fitted jointly by Fisher scoring) the shared machinery — deviance, standard errors, smoothing, reduced-rank structure — comes for free. That is exactly the classical, likelihood-based complement to the wiki's Bayesian ordinal-regression treatment (where cumulative vs. sequential are compared by Bayes factors): VGAM gives the frequentist family and a single package to fit any member. The two genuinely useful extensions to flag are reduced-rank VGLMs (stereotype / association models, dimension reduction for large category sets) and predictor-specific $x_{ij}$ covariates, which is what lets the same framework reach conditional-logit choice models. As a software paper its contribution is unification and reproducibility.