Trinomialmodeller

Trinomialmodeller is a software library and modelling framework designed to fit and analyze trinomial models for categorical data with three outcomes per trial. It is built to handle data organized as counts across three categories, and to support both basic estimation and more advanced modeling with covariates or hierarchical structure.

The core model treats each trial as yielding one of three outcomes with probabilities p1, p2, and p3, where p1 + p2 + p3 = 1. For a dataset consisting of counts n1, n2, n3 across N trials, the likelihood is multinomial with parameters p = (p1, p2, p3). In the simplest setting, maximum likelihood estimates are the observed proportions p̂i = ni / N. The framework also supports extended specifications, such as incorporating covariates through multinomial logistic links, or fitting hierarchical or mixed-effects trinomial models to account for group-level variation.

Trinomialmodeller offers features for estimation, inference, and diagnostics. It provides both frequentist and Bayesian options, including confidence intervals or credible intervals for p, likelihood-ratio tests, and information criteria for model comparison. Diagnostic tools cover goodness-of-fit measures, residual analysis, and deviance-based assessments. Visualization capabilities include ternary plots to illustrate estimated probabilities and observed proportions across groups or conditions.

The library is designed to be language-agnostic and integrates into standard data science workflows. Typical applications include marketing research on three-choice consumer preferences, genetics and ecology studies with three outcome categories, and any experimental setting with three possible results per trial.